10th class Mathematics, Chapter 2: Quadratic Equations and Inequalities MCQs

1. The type of the equation 2x² − x + 1 = 0 is:

1. (A) quadratic ✓
2. (B) linear
3. (C) third degree
4. (D) pure quadratic

2. What is the discriminant of x² + 5x − 5 = 0?

1. (A) −20
2. (B) 20
3. (C) 25
4. (D) 45 ✓

3. The solution set of 3x² − 9 = 0 is:

1. (A) {3}
2. (B) {±3}
3. (C) {±√3} ✓
4. (D) {√3}

4. Sum of the roots of 3x² + 5x − 12 = 0 is:

1. (A) 5/3
2. (B) −5/3 ✓
3. (C) 12/3
4. (D) 3/5

5. Product of the roots of 3x² + 5x − 12 = 0 is:

1. (A) −4 ✓
2. (B) 3
3. (C) 4
4. (D) 5

6. What are the roots of (x − 3)(x + 3) = 0?

1. (A) 3, −3 ✓
2. (B) 3, 3
3. (C) −3, −3
4. (D) 9, 0

7. 3 and 2 are the roots of:

1. (A) x² + 5x + 6 = 0
2. (B) x² + 6x + 5 = 0
3. (C) x² − 5x + 6 = 0 ✓
4. (D) x² + 6x − 5 = 0

8. If b² − 4ac > 0 and is a perfect square, then the roots of ax² + bx + c = 0 are:

1. (A) equal
2. (B) unequal ✓
3. (C) imaginary
4. (D) irrational

9. If b² − 4ac = 0, then the roots of ax² + bx + c = 0 are:

1. (A) unequal
2. (B) irrational
3. (C) imaginary
4. (D) equal ✓

10. The subject “c” of x − 2c = b is:

1. (A) x + b
2. (B) b − x
3. (C) (x − b)/2 ✓
4. (D) (b − x)/2

11. A quadratic equation in x has the standard form:

1. (A) ax³ + bx² + c = 0
2. (B) ax² + bx + c = 0, a = 0
3. (C) ax² + bx + c = 0, a ≠ 0 ✓
4. (D) ax + b = 0, a ≠ 0

12. The degree of a quadratic equation is:

1. (A) 3
2. (B) 0
3. (C) 2 ✓
4. (D) 1

13. If a = 0 in ax² + bx + c = 0, the equation becomes:

1. (A) quadratic
2. (B) cubic
3. (C) pure quadratic
4. (D) linear ✓

14. If b = 0 in ax² + bx + c = 0 (a ≠ 0), the equation is called:

1. (A) a cubic equation
2. (B) an identity
3. (C) a pure quadratic equation ✓
4. (D) a linear equation

15. Which of the following is a quadratic equation?

1. (A) x + 1/x³ = 0
2. (B) x² − 5x − 4 = 0 ✓
3. (C) x³ + 2x = 0
4. (D) 2x + 3 = 0

16. Every quadratic equation has at most:

1. (A) three roots
2. (B) four roots
3. (C) two roots ✓
4. (D) one root

17. The zero product property states that if AB = 0, then:

1. (A) A + B = 0
2. (B) A = B
3. (C) A = 0 or B = 0 ✓
4. (D) A = 0 and B = 0

18. The solution set of x² − 9 = 0 is:

1. (A) {−9, 9}
2. (B) {3, −3} ✓
3. (C) {3}
4. (D) {9}

19. The solution set of x² − 5x + 6 = 0 is:

1. (A) {−2, −3}
2. (B) {1, 6}
3. (C) {−1, −6}
4. (D) {2, 3} ✓

20. The roots of x(x − 4) = 0 are:

1. (A) 4 only
2. (B) −4 and 4
3. (C) 0 and 4 ✓
4. (D) 0 and −4