Class 10 Mathematics Chapter 4: Quadratic Equations — practice questions with answers
Free practice for Class 10 Mathematics, Chapter 4: Quadratic Equations. Try the solved questions below, then take a free test with instant marking and explanations.
58 questions19 easy, 25 medium, 14 hardNCERT · CBSE · State boards
Sample questions with solutions
Q1. What is the standard form of a quadratic equation in x?
- ax² + bx + c = 0, where a ≠ 0
- ax + b = 0
- ax³ + bx² + c = 0
- ax² + bx + c, with a = 0
Show answer
Answer: A. ax² + bx + c = 0, where a ≠ 0
Why: If a = 0 it is not quadratic. [p.39]
Why: If a = 0 it is not quadratic. [p.39]
Q2. The product of two consecutive positive integers is 306. Which equation models this?
- x² + x − 306 = 0
- x² − 306 = 0
- 2x + 1 = 306
- x² + 2x − 306 = 0
Show answer
Answer: A. x² + x − 306 = 0
Why: x(x + 1) = 306. [p.42]
Why: x(x + 1) = 306. [p.42]
Q3. Why is x = −12.5 rejected as the breadth of the hall?
- A length cannot be negative
- It is not a root
- It makes the area 0
- Roots must be integers
Show answer
Answer: A. A length cannot be negative
Why: Check roots against the situation. [p.44]
Why: Check roots against the situation. [p.44]
Q4. What does it mean for α to be a root of ax² + bx + c = 0?
- aα² + bα + c = 0
- α = −b/a
- α = c
- α is the coefficient of x
Show answer
Answer: A. aα² + bα + c = 0
Why: Roots are the zeroes of the polynomial. [p.39]
Why: Roots are the zeroes of the polynomial. [p.39]
Q5. What is the quadratic formula for the roots of ax² + bx + c = 0?
- x = (−b ± √(b² − 4ac)) / 2a
- x = (b ± √(b² − 4ac)) / 2a
- x = −b/2a
- x = (−b ± √(b² + 4ac)) / 2a
Show answer
Answer: A. x = (−b ± √(b² − 4ac)) / 2a
Why: Valid when b² − 4ac ≥ 0. [p.44]
Why: Valid when b² − 4ac ≥ 0. [p.44]
Q6. What is the discriminant of ax² + bx + c = 0?
- b² − 4ac
- b² + 4ac
- −b/2a
- 4ac − b²
Show answer
Answer: A. b² − 4ac
Why: It decides the nature of the roots. [p.45]
Why: It decides the nature of the roots. [p.45]
Practise all 58 questions free
Timed test, marked instantly, with the correct answer and explanation for every question and a chapter-wise report.
Start the free testUnderstand it by doing
Try the interactive Maths Lab for Class 10.
Frequently asked questions
How many practice questions are there for Class 10 Mathematics Chapter 4: Quadratic Equations?
58 questions (19 easy, 25 medium, 14 hard). A few are solved on this page; the free test shows the answer and explanation for every question after you submit.
Is this chapter from the NCERT book?
Yes — it follows the NCERT Class 10 Mathematics syllabus, used by CBSE and many state boards.