Question 1

1. What are the roots of the quadratic equation $x^2 - 5x + 6 = 0$?

A) -2, -3B) 2, 3C) -2, 3D) 2, -3

Answer

✓ Correct Answer: Option B

Question 2

2. Find the discriminant of the equation $2x^2 - 4x + 3 = 0$.

A) 8B) 16C) -8D) -16

Answer

✓ Correct Answer: Option C

Question 3

Question 4

4. Find the value of k for which $kx^2 - 2kx + 6 = 0$ ($k \neq 0$) has equal roots.

A) 6B) 0C) -6D) 4

Answer

✓ Correct Answer: Option A

Question 5

5. What is the sum of the roots of the equation $3x^2 - 12x + 5 = 0$?

A) -4B) $\frac{5}{3}$C) 4D) $-\frac{5}{3}$

Answer

✓ Correct Answer: Option C

Question 6

6. What is the product of the roots of the equation $2x^2 + 7x - 4 = 0$?

A) -2B) 2C) $\frac{7}{2}$D) $-\frac{7}{2}$

Answer

✓ Correct Answer: Option A

Question 7

7. Form a quadratic equation whose roots are 3 and -4.

A) $x^2 - x - 12 = 0$B) $x^2 + x - 12 = 0$C) $x^2 - x + 12 = 0$D) $x^2 + x + 12 = 0$

Answer

✓ Correct Answer: Option B

Question 8

8. If one root of the equation $x^2 + px + 12 = 0$ is 4, and the equation $x^2 + px + q = 0$ has equal roots, find the value of q.

A) 49B) $-\frac{49}{4}$C) $\frac{49}{4}$D) -49

Answer

✓ Correct Answer: Option C

Question 9

9. Solve for x: $\sqrt{3}x^2 + 10x + 7\sqrt{3} = 0$

A) $-\sqrt{3}, -\frac{7}{\sqrt{3}}$B) $\sqrt{3}, \frac{7}{\sqrt{3}}$C) $-\sqrt{3}, 7\sqrt{3}$D) $\sqrt{3}, -7\sqrt{3}$

Answer

✓ Correct Answer: Option A

Question 10

10. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the base length.

A) 5 cmB) 12 cmC) 7 cmD) 13 cm

Answer

✓ Correct Answer: Option B

Question 11

11. The sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the side of the larger square.

A) 12 mB) 15 mC) 18 mD) 24 m

Answer

✓ Correct Answer: Option C

Question 12

12. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

A) 30 km/hB) 40 km/hC) 45 km/hD) 50 km/h

Answer

✓ Correct Answer: Option B

Question 13

13. If the roots of $ax^2 + bx + c = 0$ are reciprocals of each other, then which relation is true?

A) a = bB) b = cC) a = 0D) a = c

Answer

✓ Correct Answer: Option D

Question 14

14. Which of the following is a quadratic equation?

A) $(x-2)^2 + 1 = 2x - 3$B) x(x+1) + 8 = (x+2)(x-2)C) $x^2 + 3x + 1 = (x-2)^2$D) $x^2 + \frac{1}{x} = 5$

Answer

✓ Correct Answer: Option A

Question 15

15. If the difference of the roots of the equation $x^2 - px + 8 = 0$ is 2, find the value of p.

A) $\pm 2$B) $\pm 4$C) $\pm 6$D) $\pm 8$

Answer

✓ Correct Answer: Option C

Question 16

16. Find the roots of the equation $3x^2 - 13x + 12 = 0$.

A) $-3, -\frac{4}{3}$B) $3, -\frac{4}{3}$C) $3, \frac{4}{3}$D) $-3, \frac{4}{3}$

Answer

✓ Correct Answer: Option C

Question 17

17. What is the discriminant of the quadratic equation $3x^2 - 2x + \frac{1}{3} = 0$?

A) 0B) 1C) 2D) -1

Answer

✓ Correct Answer: Option A

Question 18

18. The sum of a number and its reciprocal is $\frac{10}{3}$. What is the number?

A) 2 or $\frac{1}{2}$B) 3 or $\frac{1}{3}$C) 4 or $\frac{1}{4}$D) 5 or $\frac{1}{5}$

Answer

✓ Correct Answer: Option B

Question 19

19. If $\frac{1}{2}$ is a root of the equation $x^2 + kx - \frac{5}{4} = 0$, then the value of k is:

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

Answer

✓ Correct Answer: Option D

Question 20

20. Which of the following is NOT a quadratic equation?

A) $(x+2)^2 = 2(x-3)$B) $x^2 - x = (x-2)^2$C) $(x-1)^2 = 3x^2 + x - 2$D) $2x(x+3) = x^2 + 1$

Answer

✓ Correct Answer: Option B

Accepted Answer

✓ Correct Answer: Option D

Grade 10 Math Quiz: Quadratic Equations

1. What are the roots of the quadratic equation $x^2 - 5x + 6 = 0$?

2. Find the discriminant of the equation $2x^2 - 4x + 3 = 0$.

3. What is the nature of roots for the equation $x^2 + 4x + 5 = 0$?

4. Find the value of k for which $kx^2 - 2kx + 6 = 0$ ($k \neq 0$) has equal roots.

5. What is the sum of the roots of the equation $3x^2 - 12x + 5 = 0$?

6. What is the product of the roots of the equation $2x^2 + 7x - 4 = 0$?

7. Form a quadratic equation whose roots are 3 and -4.

8. If one root of the equation $x^2 + px + 12 = 0$ is 4, and the equation $x^2 + px + q = 0$ has equal roots, find the value of q.

9. Solve for x: $\sqrt{3}x^2 + 10x + 7\sqrt{3} = 0$

10. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the base length.

11. The sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the side of the larger square.

12. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

13. If the roots of $ax^2 + bx + c = 0$ are reciprocals of each other, then which relation is true?

14. Which of the following is a quadratic equation?

15. If the difference of the roots of the equation $x^2 - px + 8 = 0$ is 2, find the value of p.

16. Find the roots of the equation $3x^2 - 13x + 12 = 0$.

17. What is the discriminant of the quadratic equation $3x^2 - 2x + \frac{1}{3} = 0$?

18. The sum of a number and its reciprocal is $\frac{10}{3}$. What is the number?

19. If $\frac{1}{2}$ is a root of the equation $x^2 + kx - \frac{5}{4} = 0$, then the value of k is:

20. Which of the following is NOT a quadratic equation?