Question 1

Which of the following statements is true regarding the zeroes of a quadratic polynomial?

Accepted Answer

Correct Option: B. Solution: A quadratic polynomial can have at most two zeroes, which are the x-coordinates where the graph intersects the x-axis.

Question 2

A cubic polynomial $p(x) = x^3 - 6x^2 + 11x - 6$ is given. Which of the following values is NOT a zero of the polynomial?

Accepted Answer

Correct Option: D. Solution: The zeroes of the polynomial $x^3 - 6x^2 + 11x - 6$ can be found by factorizing it into $(x - 1)(x - 2)(x - 3) = 0$. Thus, the zeroes are $x = 1$, $x = 2$, and $x = 3$. Hence, $x = 4$ is not a zero.

Question 3

Which of the following represents the relationship between the product of zeroes and the coefficients for the quadratic polynomial $ax^2 + bx + c$?

Accepted Answer

Correct Option: A. Solution: The product of the zeroes $\alpha$ and $\beta$ of the quadratic polynomial $ax^2 + bx + c$ is given by $c/a$.

Question 4

If $p(x) = x^2 - 3x - 4$, what are the zeroes of this quadratic polynomial?

Accepted Answer

Correct Option: A. Solution: The zeroes of the polynomial $x^2 - 3x - 4$ are the values of $x$ for which $p(x) = 0$. Solving $x^2 - 3x - 4 = 0$ gives the zeroes as -1 and 4.

Question 5

If a polynomial $$q(x) = ax^4 + bx^3 + cx^2 + dx + e$$ has a degree of 4, which of the following statements is true?

Accepted Answer

Correct Option: B. Solution: A polynomial of degree $$n$$ can have at most $$n$$ zeroes. Therefore, a polynomial of degree 4 can have at most 4 zeroes.

Question 6

Consider the polynomial $p(x) = x^2 - 5x + 6$. Which of the following statements is true regarding its zeroes?

Accepted Answer

Correct Option: C. Solution: The polynomial $x^2 - 5x + 6$ can be factored as $(x-2)(x-3)$, indicating it has two distinct zeroes at $x = 2$ and $x = 3$.

Question 7

If a quadratic polynomial has zeroes at $\alpha = 2$ and $\beta = -3$, what is the polynomial?

Accepted Answer

Correct Option: A. Solution: The polynomial can be formed using the zeroes: $x^2 - (\alpha + \beta)x + \alpha\beta$. Here, $\alpha + \beta = 2 - 3 = -1$ and $\alpha\beta = 2 	imes (-3) = -6$. Thus, the polynomial is $x^2 + x - 6$.

Question 8

Which of the following represents the relationship between the zeroes and coefficients of the cubic polynomial $p(x) = 2x^3 - 4x^2 + 3x - 5$?

Accepted Answer

Correct Option: C. Solution: For a cubic polynomial $ax^3 + bx^2 + cx + d$, the sum of the zeroes is $-b/a$, the sum of the products of the zeroes taken two at a time is $c/a$, and the product of the zeroes is $-d/a$. Therefore, option c is correct.

Question 9

A cubic polynomial $r(x) = ax^3 + bx^2 + cx + d$ has zeroes at $x = 1, x = 2$, and $x = 3$. What is the sum of the zeroes of this polynomial?

Accepted Answer

Correct Option: B. Solution: The sum of the zeroes of a cubic polynomial $ax^3 + bx^2 + cx + d$ is given by $-(b/a)$. Here, the zeroes are 1, 2, and 3, so their sum is $1 + 2 + 3 = 6$.

Question 10

If the sum and product of the zeroes of a quadratic polynomial are 7 and 10 respectively, which of the following is the polynomial?

Accepted Answer

Correct Option: A. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes is $-b/a$ and the product is $c/a$. Given the sum is 7 and the product is 10, the polynomial is $x^2 - 7x + 10$.

Question 11

Consider the quadratic polynomial $p(x) = x^2 - 3x - 4$. Which of the following statements is true about its zeroes?

Accepted Answer

Correct Option: B. Solution: The zeroes of a polynomial are the x-coordinates where the graph of the polynomial intersects the x-axis.

Question 12

Consider a polynomial $p(x) = x^4 - 5x^3 + 6x^2 - 4x + 8$. What is the maximum number of zeroes this polynomial can have?

Accepted Answer

Correct Option: D. Solution: A polynomial of degree 4 can have at most 4 zeroes.

Question 13

If the zeroes of the quadratic polynomial $x^2 - 4x + 3$ are $1$ and $b2$, which of the following expressions correctly represents the relationship between the zeroes and the coefficients?

Accepted Answer

Correct Option: A. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes is $-\frac{b}{a}$ and the product is $\frac{c}{a}$. Thus, for $x^2 - 4x + 3$, $b1 + b2 = 4$ and $b1b2 = 3$.

Question 14

If a cubic polynomial is given by $p(x) = x^3 - 6x^2 + 11x - 6$, how many zeroes does it have?

Accepted Answer

Correct Option: C. Solution: A cubic polynomial can have at most 3 zeroes. The polynomial $x^3 - 6x^2 + 11x - 6$ can be factored to $(x-1)(x-2)(x-3)$, showing it has 3 zeroes.

Question 15

For the cubic polynomial $p(x) = x^3 - 6x^2 + 11x - 6$, which of the following is true about the sum of its zeroes?

Accepted Answer

Correct Option: A. Solution: The sum of the zeroes of a cubic polynomial $ax^3 + bx^2 + cx + d$ is given by $-\frac{b}{a}$. For $p(x) = x^3 - 6x^2 + 11x - 6$, the sum is $-\frac{-6}{1} = 6$.

Question 16

For the quadratic polynomial $2x^2 - 8x + 6$, what is the sum of its zeroes?

Accepted Answer

Correct Option: A. Solution: The sum of the zeroes of a quadratic polynomial $ax^2 + bx + c$ is given by $-b/a$. For $2x^2 - 8x + 6$, it is $-(-8)/2 = 4$.

Question 17

For the quadratic polynomial $x^2 + 7x + 10$, what is the relationship between the sum and product of its zeroes and its coefficients?

Accepted Answer

Correct Option: A. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes is $-b/a$ and the product is $c/a$. For $x^2 + 7x + 10$, $a=1$, $b=7$, and $c=10$, so the sum is $-7/1 = -7$ and the product is $10/1 = 10$.

Question 18

Which of the following is a quadratic polynomial?

Accepted Answer

Correct Option: A. Solution: A quadratic polynomial is of the form $ax^2 + bx + c$ where $a 
eq 0$. Option A fits this form.

Question 19

Which of the following is the standard form of a quadratic polynomial?

Accepted Answer

Correct Option: B. Solution: The standard form of a quadratic polynomial is $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers and $a 
eq 0$.

Question 20

What are the zeroes of the quadratic polynomial $x^2 - 3x - 4$?

Accepted Answer

Correct Option: A. Solution: The zeroes of the polynomial $x^2 - 3x - 4$ are the values of $x$ that make the polynomial equal to zero. By solving $x^2 - 3x - 4 = 0$, we find the zeroes are $x = -1$ and $x = 4$.

Question 21

Consider the quadratic polynomial $p(x) = x^2 - 5x + 6$. Which of the following statements is true about its zeroes?

Accepted Answer

Correct Option: A. Solution: The zeroes of the quadratic polynomial $x^2 - 5x + 6$ can be found by factoring it as $(x - 2)(x - 3) = 0$. Thus, the zeroes are $x = 2$ and $x = 3$.

Question 22

What is the maximum number of zeroes a polynomial of degree 4 can have?

Accepted Answer

Correct Option: D. Solution: A polynomial of degree $n$ can have at most $n$ zeroes. Therefore, a polynomial of degree 4 can have at most 4 zeroes.

Question 23

If the zeroes of the quadratic polynomial $x^2 - 5x + 6$ are $\alpha$ and $\beta$, what is the value of $\alpha \beta$?

Accepted Answer

Correct Option: B. Solution: The product of the zeroes of a quadratic polynomial $ax^2 + bx + c$ is given by $\frac{c}{a}$. For $x^2 - 5x + 6$, the product is $\frac{6}{1} = 6$.

Question 24

If a polynomial $p(x) = x^2 - 3x - 4$ is evaluated at $x = 2$, what is the value of $p(2)$?

Accepted Answer

Correct Option: A. Solution: Substituting $x = 2$ into $p(x) = x^2 - 3x - 4$, we get $p(2) = 2^2 - 3 	imes 2 - 4 = 4 - 6 - 4 = -6$.

Question 25

Given the sum of the zeroes of a quadratic polynomial is 5 and the product is 6, what is the quadratic polynomial?

Accepted Answer

Correct Option: A. Solution: The quadratic polynomial is of the form $x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes})$. Therefore, it is $x^2 - 5x + 6$.

Question 26

What is the geometrical meaning of the zeroes of a polynomial?

Accepted Answer

Correct Option: B. Solution: The zeroes of a polynomial are the x-coordinates where the graph of the polynomial intersects the x-axis.

Question 27

If a polynomial $q(x)$ of degree 5 has exactly 3 distinct real zeroes, what can be said about the remaining zeroes?

Accepted Answer

Correct Option: A. Solution: A polynomial of degree 5 can have at most 5 zeroes. If 3 are real and distinct, the remaining 2 must be complex, occurring in conjugate pairs.

Question 28

What is the standard form of a cubic polynomial?

Accepted Answer

Correct Option: A. Solution: A cubic polynomial is of degree 3 and its standard form is $ax^3 + bx^2 + cx + d$ where $a 
eq 0$.

Question 29

Consider the polynomial $$p(x) = 2x^3 - 4x^2 + 3x - 5$$. What is the degree of this polynomial?

Accepted Answer

Correct Option: C. Solution: The degree of a polynomial is the highest power of the variable in the polynomial. For $$p(x) = 2x^3 - 4x^2 + 3x - 5$$, the highest power of $$x$$ is 3, so the degree is 3.

Question 30

Given the cubic polynomial $p(x) = x^3 - 4x$, which of the following are the zeroes of the polynomial?

Accepted Answer

Correct Option: A. Solution: The zeroes of the polynomial $p(x) = x^3 - 4x$ are the x-coordinates where the graph intersects the x-axis, which are -2, 0, and 2.

Question 31

If the quadratic polynomial $x^2 - 3x - 4$ has zeroes $\alpha$ and $\beta$, what is the value of $\alpha + \beta$?

Accepted Answer

Correct Option: A. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes $\alpha + \beta = -\frac{b}{a}$. Here, $b = -3$ and $a = 1$, so $\alpha + \beta = 3$.

Question 32

Which of the following is a correct relationship between the zeroes and coefficients of a quadratic polynomial $ax^2 + bx + c$?

Accepted Answer

Correct Option: A. Solution: The relationships are derived from comparing the polynomial $ax^2 + bx + c$ with its factorized form $(x - \alpha)(x - \beta)$. Thus, $\alpha + \beta = -\frac{b}{a}$ and $\alpha \beta = \frac{c}{a}$.

Question 33

For the quadratic polynomial $x^2 - 3x - 4$, what are the zeroes?

Accepted Answer

Correct Option: B. Solution: The zeroes of the quadratic polynomial $x^2 - 3x - 4$ are -1 and 4, as these are the x-coordinates where the graph intersects the x-axis.

Question 34

Which of the following statements is true regarding the zeroes of a cubic polynomial?

Accepted Answer

Correct Option: A. Solution: A cubic polynomial, being of degree 3, can have at most three zeroes. This is because the graph of the polynomial can intersect the x-axis at most three times.

Question 35

Consider the quadratic polynomial $p(x) = 3x^2 - 6x + 2$. What is the sum of its zeroes?

Accepted Answer

Correct Option: A. Solution: The sum of the zeroes of a quadratic polynomial $ax^2 + bx + c$ is given by $-\frac{b}{a}$. For $p(x) = 3x^2 - 6x + 2$, the sum is $-\frac{-6}{3} = 2$.

Question 36

For the quadratic polynomial $p(x) = x^2 + 7x + 10$, what is the relationship between the sum and product of its zeroes and its coefficients?

Accepted Answer

Correct Option: A. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes is $-b/a$ and the product is $c/a$. For $x^2 + 7x + 10$, this holds true.

Question 37

For the quadratic polynomial $p(x) = x^2 - 3x - 4$, what is the sum of its zeroes?

Accepted Answer

Correct Option: A. Solution: The sum of the zeroes of a quadratic polynomial $ax^2 + bx + c$ is given by $-b/a$. For $x^2 - 3x - 4$, the sum is $-(-3)/1 = 3$.

Question 38

What is the degree of the polynomial $5x^3 - 4x^2 + x\sqrt{2}$?

Accepted Answer

Correct Option: C. Solution: The degree of a polynomial is the highest power of the variable. Here, the highest power of $x$ is 3.

Question 39

For the polynomial $p(x) = 2x^2 - 4x + 2$, determine the relationship between its zeroes and coefficients.

Accepted Answer

Correct Option: A. Solution: For the polynomial $2x^2 - 4x + 2$, the sum of zeroes is $-\frac{-4}{2} = 2$, and the product of zeroes is $\frac{2}{2} = 1$. Therefore, the correct relationship is that the sum of zeroes is $2$ and the product of zeroes is $1$.

Question 40

Given that the sum and product of the zeroes of a quadratic polynomial are -5 and 6 respectively, which of the following is the correct quadratic polynomial?

Accepted Answer

Correct Option: B. Solution: The quadratic polynomial can be formed using the relation $x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes})$. Substituting the given values, we get $x^2 - (-5)x + 6 = x^2 + 5x + 6$.

Question 41

A quadratic polynomial has a sum of zeroes equal to 7 and a product of zeroes equal to 10. Which of the following polynomials matches these conditions?

Accepted Answer

Correct Option: A. Solution: Using the formula for forming a quadratic polynomial: $x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes})$, we substitute the given values to get $x^2 - 7x + 10$.

Question 42

Consider the cubic polynomial $p(x) = x^3 - 4x$. How many zeroes does this polynomial have?

Accepted Answer

Correct Option: C. Solution: A cubic polynomial can have at most 3 zeroes. For $x^3 - 4x$, the zeroes are $-2$, $0$, and $2$, as these are the x-coordinates where the graph intersects the x-axis.

Question 43

Consider the polynomial $p(x) = ax^3 + bx^2 + cx + d$. If the sum of the zeroes is 5, the sum of the product of the zeroes taken two at a time is -6, and the product of the zeroes is -8, what are the values of $a$, $b$, $c$, and $d$?

Accepted Answer

Correct Option: A. Solution: For a cubic polynomial $ax^3 + bx^2 + cx + d$, the relationships are: sum of zeroes $= -\frac{b}{a}$, sum of the product of zeroes taken two at a time $= \frac{c}{a}$, and product of zeroes $= -\frac{d}{a}$. Solving these gives $a = 1, b = -5, c = -6, d = -8$.

Question 44

The zeroes of a quadratic polynomial are always real numbers.

Accepted Answer

Answer: False. Solution: The zeroes of a quadratic polynomial can be complex numbers if the discriminant is negative.

Question 45

A polynomial of degree 3 is called a cubic polynomial.

Accepted Answer

Answer: True. Solution: A polynomial of degree 3 is indeed called a cubic polynomial, as it is defined by the highest power of the variable being 3.

Question 46

A quadratic polynomial can be formed if the sum and product of its zeroes are known.

Accepted Answer

Answer: True. Solution: If the sum and product of the zeroes of a quadratic polynomial are given, the polynomial can be expressed as $x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes})$. This allows for the construction of the polynomial.

Question 47

A quadratic polynomial can have more than two zeroes.

Accepted Answer

Answer: False. Solution: A quadratic polynomial can have at most two zeroes, as it is a polynomial of degree 2.

Question 48

A quadratic polynomial can have at most two zeroes, and these zeroes are the x-coordinates of the points where the parabola intersects the x-axis.

Accepted Answer

Answer: True. Solution: A quadratic polynomial is of the form $ax^2 + bx + c$ and its graph is a parabola. The zeroes of the polynomial are the x-coordinates where the parabola intersects the x-axis. This is confirmed in the excerpt where it is stated that a quadratic polynomial has at most two zeroes.

Question 49

A polynomial of degree 2 is called a quadratic polynomial.

Accepted Answer

Answer: True. Solution: A polynomial of degree 2 is indeed called a quadratic polynomial, as it involves the square of the variable.

Question 50

The zeroes of a cubic polynomial are unrelated to its coefficients.

Accepted Answer

Answer: False. Solution: The zeroes of a cubic polynomial are related to its coefficients through the relationships: sum of zeroes = $-b/a$, sum of products of zeroes taken two at a time = $c/a$, and product of zeroes = $-d/a$.

Question 51

The zeroes of a polynomial are the x-coordinates of the points where its graph intersects the x-axis.

Accepted Answer

Answer: True. Solution: The zeroes of a polynomial $p(x)$ are precisely the x-coordinates of the points where the graph of $y = p(x)$ intersects the x-axis.

Question 52

A polynomial of degree 2 can have at most two zeroes.

Accepted Answer

Answer: True. Solution: A polynomial of degree 2 is a quadratic polynomial, and its graph can intersect the x-axis at most two times, corresponding to its zeroes.

Question 53

A cubic polynomial $ax^3 + bx^2 + cx + d$ can have more than three zeroes.

Accepted Answer

Answer: False. Solution: A cubic polynomial of the form $ax^3 + bx^2 + cx + d$ has at most three zeroes, as the degree of the polynomial determines the maximum number of zeroes.

Question 54

The zeroes of a polynomial are the x-coordinates where the graph of the polynomial intersects the x-axis.

Accepted Answer

Answer: True. Solution: The zeroes of a polynomial are indeed the x-coordinates where the graph intersects the x-axis, as this is the point where the polynomial evaluates to zero.

Question 55

The standard form of a quadratic polynomial is $ax^2 + bx + c$, where $a, b, c$ are real numbers and $a 
eq 0$.

Accepted Answer

Answer: True. Solution: The standard form of a quadratic polynomial is $ax^2 + bx + c$, where $a, b, c$ are real numbers and $a 
eq 0$, ensuring the degree is 2.

Question 56

A polynomial of degree 1 is called a linear polynomial.

Accepted Answer

Answer: True. Solution: A polynomial of degree 1 is indeed called a linear polynomial, as it is defined by the highest power of the variable being 1.

Question 57

The sum and product of the zeroes of a quadratic polynomial $ax^2 + bx + c$ are given by $-\frac{b}{a}$ and $\frac{c}{a}$ respectively.

Accepted Answer

Answer: True. Solution: The relationship between the zeroes of a quadratic polynomial and its coefficients is given by the formulas: sum of zeroes $\alpha + \beta = -\frac{b}{a}$ and product of zeroes $\alpha \beta = \frac{c}{a}$. This is derived from comparing the polynomial with its factorized form.

Question 58

A polynomial of degree 2 is always called a quadratic polynomial, and it can have at most two zeroes.

Accepted Answer

Answer: True. Solution: A polynomial of degree 2 is defined as a quadratic polynomial, and it can have at most two zeroes as indicated by its degree.

Question 59

The sum of the zeroes of a quadratic polynomial $ax^2 + bx + c$ is given by $-\frac{b}{a}$.

Accepted Answer

Answer: True. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes is $\alpha + \beta = -\frac{b}{a}$, as derived from comparing coefficients.

Question 60

A polynomial of degree 2 is always in the standard form $ax^2 + bx + c$, where $a 
eq 0$.

Accepted Answer

Answer: True. Solution: A quadratic polynomial is defined as having a degree of 2 and is generally expressed in the standard form $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers and $a 
eq 0$.

Question 61

The quadratic polynomial with zeroes having a sum of $-3$ and a product of $2$ is $x^2 + 3x + 2$.

Accepted Answer

Answer: True. Solution: Given the sum of zeroes $\alpha + \beta = -3$ and the product $\alpha \beta = 2$, the quadratic polynomial is $x^2 - (\alpha + \beta)x + \alpha \beta = x^2 + 3x + 2$.

Question 62

A cubic polynomial can have more than three zeroes.

Accepted Answer

Answer: False. Solution: A polynomial of degree 3 can have at most three zeroes, as the graph of $y = p(x)$ intersects the x-axis at most three times.

Question 63

The sum of the zeroes of a quadratic polynomial $ax^2 + bx + c$ is given by $-\frac{b}{a}$.

Accepted Answer

Answer: True. Solution: For a quadratic polynomial $ax^2 + bx + c$, the sum of the zeroes $\alpha$ and $\beta$ is $\alpha + \beta = -\frac{b}{a}$, which is derived from the relationship between the coefficients and zeroes of the polynomial.

Question 64

A polynomial of degree 4 can have at most 4 zeroes.

Accepted Answer

Answer: True. Solution: According to the fundamental theorem of algebra, a polynomial of degree $n$ can have at most $n$ zeroes. Therefore, a polynomial of degree 4 can have at most 4 zeroes.

Polynomials

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Degree of Polynomials

Zeroes of Polynomials

Geometrical Meaning of Zeroes

Relationship between Zeroes and Coefficients

Polynomial Factorization

Graphical Representation of Polynomials

Summary

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Degree of Polynomials

Zeroes of Polynomials

Geometrical Meaning of Zeroes

Relationship between Zeroes and Coefficients

Polynomial Factorization

Graphical Representation of Polynomials

General Tips

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Multiple Choice Questions

Q1.Which of the following statements is true regarding the zeroes of a quadratic polynomial?

Correct Answer: B

Q2.A cubic polynomial p(x)=x3−6x2+11x−6p(x) = x^3 - 6x^2 + 11x - 6p(x)=x3−6x2+11x−6 is given. Which of the following values is NOT a zero of the polynomial?

Correct Answer: D

Q3.Which of the following represents the relationship between the product of zeroes and the coefficients for the quadratic polynomial ax2+bx+cax^2 + bx + cax2+bx+c?

Correct Answer: A

Q4.If p(x)=x2−3x−4p(x) = x^2 - 3x - 4p(x)=x2−3x−4, what are the zeroes of this quadratic polynomial?

Correct Answer: A

Q5.If a polynomial q(x)=ax4+bx3+cx2+dx+eq(x) = ax^4 + bx^3 + cx^2 + dx + eq(x)=ax4+bx3+cx2+dx+e has a degree of 4, which of the following statements is true?

Correct Answer: B

Q6.Consider the polynomial p(x)=x2−5x+6p(x) = x^2 - 5x + 6p(x)=x2−5x+6. Which of the following statements is true regarding its zeroes?

Correct Answer: C

Q7.If a quadratic polynomial has zeroes at α=2\alpha = 2α=2 and β=−3\beta = -3β=−3, what is the polynomial?

Correct Answer: A

Q8.Which of the following represents the relationship between the zeroes and coefficients of the cubic polynomial p(x)=2x3−4x2+3x−5p(x) = 2x^3 - 4x^2 + 3x - 5p(x)=2x3−4x2+3x−5?

Correct Answer: C

Q9.A cubic polynomial r(x)=ax3+bx2+cx+dr(x) = ax^3 + bx^2 + cx + dr(x)=ax3+bx2+cx+d has zeroes at x=1,x=2x = 1, x = 2x=1,x=2, and x=3x = 3x=3. What is the sum of the zeroes of this polynomial?

Correct Answer: B

Q10.If the sum and product of the zeroes of a quadratic polynomial are 7 and 10 respectively, which of the following is the polynomial?

Correct Answer: A

Q11.Consider the quadratic polynomial p(x)=x2−3x−4p(x) = x^2 - 3x - 4p(x)=x2−3x−4. Which of the following statements is true about its zeroes?

Correct Answer: B

Q12.Consider a polynomial p(x)=x4−5x3+6x2−4x+8p(x) = x^4 - 5x^3 + 6x^2 - 4x + 8p(x)=x4−5x3+6x2−4x+8. What is the maximum number of zeroes this polynomial can have?

Correct Answer: D

Q13.If the zeroes of the quadratic polynomial x2−4x+3x^2 - 4x + 3x2−4x+3 are 1 and b2, which of the following expressions correctly represents the relationship between the zeroes and the coefficients?

Correct Answer: A

Q14.If a cubic polynomial is given by p(x)=x3−6x2+11x−6p(x) = x^3 - 6x^2 + 11x - 6p(x)=x3−6x2+11x−6, how many zeroes does it have?

Correct Answer: C

Q15.For the cubic polynomial p(x)=x3−6x2+11x−6p(x) = x^3 - 6x^2 + 11x - 6p(x)=x3−6x2+11x−6, which of the following is true about the sum of its zeroes?

Correct Answer: A

Q16.For the quadratic polynomial 2x2−8x+62x^2 - 8x + 62x2−8x+6, what is the sum of its zeroes?

Correct Answer: A

Q17.For the quadratic polynomial x2+7x+10x^2 + 7x + 10x2+7x+10, what is the relationship between the sum and product of its zeroes and its coefficients?

Correct Answer: A

Q18.Which of the following is a quadratic polynomial?

Correct Answer: A

Q19.Which of the following is the standard form of a quadratic polynomial?

Correct Answer: B

Q20.What are the zeroes of the quadratic polynomial x2−3x−4x^2 - 3x - 4x2−3x−4?

Correct Answer: A

Q21.Consider the quadratic polynomial p(x)=x2−5x+6p(x) = x^2 - 5x + 6p(x)=x2−5x+6. Which of the following statements is true about its zeroes?

Correct Answer: A

Q22.What is the maximum number of zeroes a polynomial of degree 4 can have?

Correct Answer: D

Q23.If the zeroes of the quadratic polynomial x2−5x+6x^2 - 5x + 6x2−5x+6 are α\alphaα and β\betaβ, what is the value of αβ\alpha \betaαβ?

Correct Answer: B

Q24.If a polynomial p(x)=x2−3x−4p(x) = x^2 - 3x - 4p(x)=x2−3x−4 is evaluated at x=2x = 2x=2, what is the value of p(2)p(2)p(2)?

Correct Answer: A

Q25.Given the sum of the zeroes of a quadratic polynomial is 5 and the product is 6, what is the quadratic polynomial?

Correct Answer: A

Q26.What is the geometrical meaning of the zeroes of a polynomial?