Grade 10 Math Quiz: Quadratic Equations | Concept of Maths

Question 1

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

A) \( -2, -3 \)

B) \( 2, 3 \)

C) \( -2, 3 \)

D) \( 2, -3 \)

Answer

Correct Answer: B

Question 2

2. Find the discriminant of the equation \( 2x^2 - 4x + 3 = 0 \).

A) \( 8 \)

B) \( 16 \)

C) \( -8 \)

D) \( -16 \)

Answer

Correct Answer: C

Question 3

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

A) Real and distinct

B) Real and equal

C) Real and rational

D) No real roots

Answer

Correct Answer: D

Question 4

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

A) 6

B) 0

C) -6

D) 4

Answer

Correct Answer: A

Question 5

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

Question 6

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

A) -2

B) 2

C) \( \frac{7}{2} \)

D) \( -\frac{7}{2} \)

Answer

Correct Answer: 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: 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) 49

B) \( -\frac{49}{4} \)

C) \( \frac{49}{4} \)

D) -49

Answer

Correct Answer: 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: 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 cm

B) 12 cm

C) 7 cm

D) 13 cm

Answer

Correct Answer: 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 m

B) 15 m

C) 18 m

D) 24 m

Answer

Correct Answer: 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/h

B) 40 km/h

C) 45 km/h

D) 50 km/h

Answer

Correct Answer: B

Question 13

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

A) \( a = b \)

B) \( b = c \)

C) \( a = 0 \)

D) \( a = c \)

Answer

Correct Answer: 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: 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: 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: C

Question 17

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

A) 0

B) 1

C) 2

D) -1

Answer

Correct Answer: 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: 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) -2

B) -1

C) 1

D) 2

Answer

Correct Answer: 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: B

Accepted Answer

Correct Answer: C

Master Quadratic Equations: Grade 10 Math Quiz | Concept of Maths

Master Quadratic Equations: Grade 10 Math Quiz | Concept of Maths

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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?

Grade 10 Math Quiz: Quadratic Equations | Concept of Maths

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 \( 3x^2 - 12x + 5 = 0 \)?

Master Quadratic Equations: Grade 10 Math Quiz | Concept of Maths

Master Quadratic Equations: Grade 10 Math Quiz | Concept of Maths

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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?