Question 1

1. The sum and product of the zeroes of the polynomial $x^2 - 5x + 6$ are respectively:

A) -5, 6B) 5, 6C) 6, 5D) -6, -5

Answer

✓ Correct Answer: Option B

Question 2

2. A quadratic polynomial whose zeroes are 3 and -2 is:

A) $x^2 - x + 6$B) $x^2 + x - 6$C) $x^2 - x - 6$D) $x^2 + x + 6$

Answer

✓ Correct Answer: Option C

Question 3

Question 4

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

A) 1B) 2C) 3D) 4

Answer

✓ Correct Answer: Option C

Question 5

5. The graph of y = p(x) intersects the x-axis at 3 distinct points and touches it at 2 distinct points. The total number of distinct zeroes of p(x) is:

A) 3B) 2C) 5D) 0

Answer

✓ Correct Answer: Option C

Question 6

6. If one zero of the polynomial $f(x) = x^2 - 4x + k$ is 2, then the value of k is:

A) 2B) 4C) -4D) 8

Answer

✓ Correct Answer: Option B

Question 7

7. If $\alpha$ and $\beta$ are the zeroes of the polynomial $f(x) = x^2 - px + q$, what is the value of $\frac{1}{\alpha} + \frac{1}{\beta}$?

A) $\frac{p}{q}$B) $\frac{q}{p}$C) $-\frac{p}{q}$D) $-\frac{q}{p}$

Answer

✓ Correct Answer: Option A

Question 8

8. When the polynomial $2x^2 + 3x + 1$ is divided by x + 2, the remainder is:

A) 1B) -1C) 3D) -3

Answer

✓ Correct Answer: Option C

Question 9

9. If the sum of the zeroes of the polynomial $kx^2 + 2x + 3k$ is equal to their product, find the value of k.

A) $\frac{2}{3}$B) $-\frac{2}{3}$C) $\frac{3}{2}$D) $-\frac{3}{2}$

Answer

✓ Correct Answer: Option B

Question 10

10. If one zero of the polynomial $3x^2 + 8x + k$ is the reciprocal of the other, then the value of k is:

A) 3B) -3C) $\frac{1}{3}$D) $-\frac{1}{3}$

Answer

✓ Correct Answer: Option A

Question 11

11. Find the quadratic polynomial whose sum and product of zeroes are $\sqrt{2}$ and $-\frac{3}{2}$ respectively.

A) $2x^2 - 2\sqrt{2}x - 3$B) $2x^2 + 2\sqrt{2}x - 3$C) $x^2 - \sqrt{2}x + 3$D) $2x^2 - \sqrt{2}x + 3$

Answer

✓ Correct Answer: Option A

Question 12

12. If $\alpha$ and $\beta$ are the zeroes of $x^2 - x - 4$, find the value of $\alpha^2 + \beta^2$.

A) 7B) 8C) 9D) 10

Answer

✓ Correct Answer: Option C

Question 13

13. The polynomial $x^3 - 3x^2 + x + 1$ has zeroes a-b, a, and a+b. Find the value of a.

A) 1B) -1C) 2D) -2

Answer

✓ Correct Answer: Option A

Question 14

14. Which of the following algebraic expressions is NOT a polynomial?

A) $x^2 + 2x + 1$B) $\sqrt{2}x^2 - 3x + 5$C) $2x + \frac{3}{x}$D) $x^3 - 4$

Answer

✓ Correct Answer: Option C

Question 15

15. If the product of the zeroes of $x^2 - 3kx + 2k^2 - 1$ is 7, and k > 0, find k.

A) 2B) 3C) 4D) 1

Answer

✓ Correct Answer: Option A

Question 16

16. If $p(x) = x^2 - 2\sqrt{2}x + 1$, what is the value of $p(2\sqrt{2})$?

A) 0B) 1C) $4\sqrt{2}$D) 8

Answer

✓ Correct Answer: Option B

Question 17

17. What is the condition for the zeroes of $ax^2 + bx + c$ to be equal in magnitude but opposite in sign?

A) c = 0B) a = 0C) b = 0D) b = c

Answer

✓ Correct Answer: Option C

Question 18

18. A real number $\alpha$ is a zero of the polynomial p(x) if and only if:

A) $p(\alpha) > 0$B) $p(\alpha) < 0$C) $p(\alpha) = 1$D) $p(\alpha) = 0$

Answer

✓ Correct Answer: Option D

Question 19

19. If $\alpha$ and $\beta$ are the zeroes of $f(x) = x^2 - p(x+1) - c$, then the value of $(\alpha+1)(\beta+1)$ is:

A) 1 - cB) c - 1C) 1 + cD) c

Answer

✓ Correct Answer: Option A

Question 20

20. The geometric representation of the graph of a quadratic polynomial is a:

A) Straight lineB) CircleC) ParabolaD) Ellipse

Answer

✓ Correct Answer: Option C

Accepted Answer

✓ Correct Answer: Option B

Grade 10 Maths: Polynomials Interactive Quiz

1. The sum and product of the zeroes of the polynomial $x^2 - 5x + 6$ are respectively:

2. A quadratic polynomial whose zeroes are 3 and -2 is:

3. If $\alpha$ and $\beta$ are the zeroes of the polynomial $2x^2 + 5x + 1$, find the value of $\alpha + \beta + \alpha\beta$.

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

5. The graph of y = p(x) intersects the x-axis at 3 distinct points and touches it at 2 distinct points. The total number of distinct zeroes of p(x) is:

6. If one zero of the polynomial $f(x) = x^2 - 4x + k$ is 2, then the value of k is:

7. If $\alpha$ and $\beta$ are the zeroes of the polynomial $f(x) = x^2 - px + q$, what is the value of $\frac{1}{\alpha} + \frac{1}{\beta}$?

8. When the polynomial $2x^2 + 3x + 1$ is divided by x + 2, the remainder is:

9. If the sum of the zeroes of the polynomial $kx^2 + 2x + 3k$ is equal to their product, find the value of k.

10. If one zero of the polynomial $3x^2 + 8x + k$ is the reciprocal of the other, then the value of k is:

11. Find the quadratic polynomial whose sum and product of zeroes are $\sqrt{2}$ and $-\frac{3}{2}$ respectively.

12. If $\alpha$ and $\beta$ are the zeroes of $x^2 - x - 4$, find the value of $\alpha^2 + \beta^2$.

13. The polynomial $x^3 - 3x^2 + x + 1$ has zeroes a-b, a, and a+b. Find the value of a.

14. Which of the following algebraic expressions is NOT a polynomial?

15. If the product of the zeroes of $x^2 - 3kx + 2k^2 - 1$ is 7, and k > 0, find k.

16. If $p(x) = x^2 - 2\sqrt{2}x + 1$, what is the value of $p(2\sqrt{2})$?

17. What is the condition for the zeroes of $ax^2 + bx + c$ to be equal in magnitude but opposite in sign?

18. A real number $\alpha$ is a zero of the polynomial p(x) if and only if:

19. If $\alpha$ and $\beta$ are the zeroes of $f(x) = x^2 - p(x+1) - c$, then the value of $(\alpha+1)(\beta+1)$ is:

20. The geometric representation of the graph of a quadratic polynomial is a: