Class 10 Quadratic Equations Worksheet

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Curriculum note: Quadratic Equations is a unit in the CBSE Class 10 Mathematics syllabus for 2026-27, which covers solving by factorisation and by the quadratic formula (real roots only), and the NCERT Class 10 Mathematics textbook. Sum and product of roots is a related idea. This quiz is original practice, not an official paper.

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Class 10 Quadratic Equations – Practice Worksheet

Name:

Date:

Marks: / 10

Instructions: Answer all 10 questions. Circle the correct option and show your working in the space given.

Which of these is a quadratic equation?
- (A) x³ − 4 = 0
- (B) x² − 4 = 0
- (C) x − 4 = 0
- (D) x⁴ = 4
Working:
Answer:
What are the roots of x² − 5x + 6 = 0?
- (A) −2 and −3
- (B) 1 and 6
- (C) 2 and 3
- (D) −1 and 6
Working:
Answer:
What is the discriminant of x² + 4x + 4 = 0?
- (A) 0
- (B) 8
- (C) 32
- (D) −16
Working:
Answer:
Solve: x² − 9 = 0
- (A) x = 9 only
- (B) x = 3 only
- (C) x = −9 or x = 9
- (D) x = 3 or x = −3
Working:
Answer:
What is the nature of the roots of x² + x + 1 = 0?
- (A) Two distinct real roots
- (B) Two equal real roots
- (C) No real roots
- (D) Exactly one real root
Working:
Answer:
Use the quadratic formula to solve x² − 2x − 3 = 0.
- (A) x = −3 or x = 1
- (B) x = 3 or x = −1
- (C) x = 3 or x = 1
- (D) x = −3 or x = −1
Working:
Answer:
What is the sum of the roots of x² − 7x + 10 = 0?
- (A) −7
- (B) 10
- (C) 3
- (D) 7
Working:
Answer:
What is the product of the roots of 2x² − 8x + 6 = 0?
- (A) 3
- (B) 6
- (C) 4
- (D) −3
Working:
Answer:
For what positive value of k does x² + kx + 9 = 0 have equal roots?
- (A) k = 3
- (B) k = 9
- (C) k = 6
- (D) k = 12
Working:
Answer:
The product of two consecutive positive integers is 56. What are they?
- (A) 6 and 7
- (B) 8 and 9
- (C) 5 and 6
- (D) 7 and 8
Working:
Answer:

Original questions by LearnWise Practice Hub.

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Class 10 Quadratic Equations – Answer Key

Answer: (B) x² − 4 = 0
A quadratic equation has the highest power of x equal to 2. Only x² − 4 = 0 fits.
Answer: (C) 2 and 3
Factorise: x² − 5x + 6 = (x − 2)(x − 3). Setting each factor to zero gives x = 2 and x = 3.
Answer: (A) 0
Here a = 1, b = 4, c = 4. D = b² − 4ac = 16 − 16 = 0, so the roots are real and equal.
Answer: (D) x = 3 or x = −3
x² = 9, so x = ±3. Or factorise: (x − 3)(x + 3) = 0.
Answer: (C) No real roots
a = 1, b = 1, c = 1, so D = 1 − 4 = −3. Since D < 0 the equation has no real roots.
Answer: (B) x = 3 or x = −1
a = 1, b = −2, c = −3, so D = 4 + 12 = 16 and √D = 4. Then x = (2 ± 4)/2, giving x = 3 or x = −1.
Answer: (D) 7
The equation factorises as (x − 2)(x − 5) = 0, so the roots are 2 and 5. Their sum is 7.
Answer: (A) 3
Divide by 2: x² − 4x + 3 = 0 = (x − 1)(x − 3). The roots are 1 and 3, and their product is 3.
Answer: (C) k = 6
Equal roots need D = 0: k² − 4 × 1 × 9 = 0, so k² = 36 and k = 6 (positive value).
Answer: (D) 7 and 8
Let the integers be x and x + 1. Then x(x + 1) = 56, so x² + x − 56 = 0, which factorises as (x + 8)(x − 7) = 0. x = 7 (positive), so the numbers are 7 and 8.

Class 10 Quadratic Equations Worksheet

Class 10 Quadratic Equations – Answer Key

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