Quadratic Equations is one of the most reliable mark-earners in the Class 10 board paper. Once your child is fluent with factorising, the discriminant, and the sum and product of roots, a whole family of questions becomes routine — including the word problems (consecutive integers, a number and its reciprocal) that look hard but reduce to a neat quadratic. Short, regular practice is what turns “I think I can” into “I’ve got this”.

This free printable worksheet has 12 questions from Bmathpro’s own question bank of 10,500+ validated maths questions — the same bank our enrolled students practise from. Every answer comes with a one-line explanation, so you can check your child’s method, not just the final answer.

Set aside 15–20 minutes, keep the answers hidden until the end, and let your child attempt every question — a wrong attempt tells you more than a skipped one.

What this worksheet covers

• Solving quadratics by factorising
• Sum and product of roots (−b/a and c/a)
• The discriminant b² − 4ac
• The nature of roots (real and distinct, equal, or not real)
• Word problems that form a quadratic equation

Maps to the CBSE Class 10 Quadratic Equations chapter (NCERT) and equivalent ICSE/State-board units.

Class 10 Quadratic Equations Worksheet — 12 Questions

Warm-up

1. Find the sum of the roots of the quadratic equation x² − 7x + 12 = 0. (Write your answer.)

2. Solve x² − 7x + 10 = 0 and give the larger root. (Write your answer.)

3. Find the discriminant of the quadratic equation x² − 5x + 6 = 0. (Write your answer.)

Building up

4. Find the larger root of x² − 5x − 14 = 0. (Write your answer.)

5. For x² − 10x + 9 = 0, what is the product of the roots? (Write your answer.)

6. Find the discriminant of x² + 7x + 3. (Write your answer.)

7. What is the nature of the roots of 2x² + 3x + 5 = 0?
A. Two distinct real roots  B. Two equal real roots  C. No real roots  D. One real root

8. How many real roots does x² + 4x + 4 = 0 have?
A. Two distinct  B. None  C. One (repeated)  D. Infinitely many

Challenge

9. Solve x² − 12x + 32 = 0 and give the larger root. (Write your answer.)

10. The product of two consecutive positive integers is 56. Find the smaller integer. (Write your answer.)

11. The product of two consecutive positive odd integers is 143. Form n(n + 2) = 143 and solve for the smaller integer n. (Write your answer.)

12. The sum of a positive number greater than 1 and its reciprocal is 2.5. Find the number. (Write your answer.)

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Answer key with explanations

Show answers and explanations (parents — open this after your child finishes)

1. 7 — roots 3 and 4; sum = 7 (also −b/a = 7).
2. 5 — (x−2)(x−5), roots 2 and 5; larger is 5.
3. 1 — D = 25 − 24 = 1.
4. 7 — (x−7)(x+2), roots 7 and −2; larger is 7.
5. 9 — product of roots = c/a = 9.
6. 37 — D = 49 − 12 = 37.
7. C. No real roots — D = 9 − 40 = −31 < 0.
8. C. One (repeated) — D = 16 − 16 = 0 (x = −2).
9. 8 — (x−4)(x−8), roots 4 and 8; larger is 8.
10. 7 — n²+n−56 = (n−7)(n+8), so n = 7.
11. 11 — n²+2n−143 = (n+13)(n−11), so n = 11 (11 and 13).
12. 2 — 2x²−5x+2 = (2x−1)(x−2), so x = 2 (x > 1).

How to use this worksheet at home

• Keep it short and calm. 15–20 minutes beats an hour of pressure.
• Check the discriminant first. On “nature of roots” questions, ask your child to work out b² − 4ac before anything else — it answers the question in one step.
• Praise the method, not the marks. (We deliberately don’t put marks on our worksheets.)

FAQs

Is this worksheet free to print?
Yes — free to use and print at home, no sign-up needed.

Which syllabus does it follow?
Standard Class 10 Quadratic Equations chapter — CBSE (NCERT), ICSE and State boards.

What does the discriminant actually tell you?
b² − 4ac decides the nature of the roots: positive → two distinct real roots, zero → one repeated real root, negative → no real roots. It answers “nature of roots” questions without solving the equation. A free demo class shows the shortcut.

Where can my child get more practice like this?
Enrolled students get Math Gym, our paid practice app with 10,500+ questions — see our courses page.

Also practise: Real Numbers · Arithmetic Progressions · all Class 10 worksheets.

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