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Class 10 Quadratic Equations: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 4, Quadratic Equations, each with a worked answer. They cover the four things the chapter asks of you: solving by factorisation, finding a value that gives equal roots, using the discriminant to say whether real roots exist, and turning a word problem into an equation. Try each one on paper before you open the answer.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us. For the explanation behind each method, read our guide to NCERT Class 10 Chapter 4, Quadratic Equations.
What the chapter says you need
Four facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 4, printed pages 38 to 47) cover every question below:
- A quadratic equation can be written as ax² + bx + c = 0 with a ≠ 0: the standard form (section 4.2, page 39).
- To solve by factorisation, split the middle term, write the left side as two brackets, and put each bracket equal to zero (section 4.3, page 42 onwards).
- The discriminant is b² − 4ac. If it is greater than 0 there are two distinct real roots; if it equals 0, two equal real roots; if it is less than 0, no real roots (section 4.4, pages 44 and 45).
- The quadratic formula gives the roots as x = (−b ± √(b² − 4ac)) / 2a, when b² − 4ac ≥ 0 (summary, section 4.5, page 47).
For the board paper, CBSE's 2026-27 Class 10 Maths curriculum limits quadratic equations to real roots only (curriculum, page 4).
Factorisation
Question 1. Find the positive root of x² − 2x − 15 = 0.
Answer: x² − 2x − 15 = (x − 5)(x + 3) = 0, so x = 5 or x = −3. The positive root is 5. Check: 25 − 10 − 15 = 0.
Question 2. Find the positive root of x² + x − 12 = 0.
Answer: x² + x − 12 = (x + 4)(x − 3) = 0, so x = −4 or x = 3. The positive root is 3. Check: 9 + 3 − 12 = 0.
Question 3. Find the roots of x² − 5x + 6 = 0.
Answer: x² − 5x + 6 = (x − 2)(x − 3) = 0, so the roots are 2 and 3. Check: 4 − 10 + 6 = 0 and 9 − 15 + 6 = 0.
The discriminant
Question 4. What is the discriminant of 2x² − 4x + 3 = 0? Does it have real roots?
Answer: Here a = 2, b = −4, c = 3. b² − 4ac = 16 − 24 = −8. It is negative, so there are no real roots.
Question 5. For what value of k does x² − 6x + k = 0 have two equal roots?
Answer: Equal roots need b² − 4ac = 0: 36 − 4k = 0, so k = 9. Check: x² − 6x + 9 = (x − 3)², so both roots are 3.
Question 6. Does x² + 6x + 9 = 0 have real roots? If so, find them.
Answer: b² − 4ac = 36 − 36 = 0, so it has two equal real roots. x² + 6x + 9 = (x + 3)² = 0, so both roots are −3.
Word problems
For a word problem: call the unknown x, write the other quantities in terms of x, use the one fact the question gives, and put the equation in standard form. Then reject any root that makes no sense (a negative length or speed).
Question 7. Two consecutive positive integers multiply to give 132. What is the smaller one?
Answer: Let the smaller be x; the next is x + 1. Then x(x + 1) = 132, so x² + x − 132 = 0, which factorises as (x + 12)(x − 11) = 0. The positive answer is x = 11 (and 11 × 12 = 132).
Question 8. A cyclist rides 120 km at a steady speed. Had she ridden 2 km per hour faster, the trip would have taken 2 hours less. What is her usual speed, in km per hour?
Answer: Let the speed be x km/h. The time is 120/x, and 120/x − 120/(x + 2) = 2. Then 120(x + 2) − 120x = 2x(x + 2), so 240 = 2x² + 4x, which gives x² + 2x − 120 = 0, that is (x + 12)(x − 10) = 0. A speed cannot be negative, so x = 10 km/h. Check: 120 ÷ 10 = 12 hours, and 120 ÷ 12 = 10 hours, which is 2 hours less.
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Quadratic Equations questions. Questions 1, 2, 4, 5, 7 and 8 above are in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- When you are ready for the board style, see how CBSE splits the marks in our Class 10 Maths syllabus 2026-27 guide.
If you use an AI chatbot to check a solution, put its answer back into the equation first, as in our guide to checking an AI's maths answers.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are printed page numbers of the textbook unless marked as PDF pages.
- NCERT, Mathematics, Textbook for Class X, Chapter 4 "Quadratic Equations" (Reprint 2026-27), printed pages 38-47 (standard form, section 4.2, page 39; factorisation, section 4.3, page 42 onwards; nature of roots and the discriminant, section 4.4, pages 44-45; quadratic formula and summary, section 4.5, page 47): ncert.nic.in/textbook/pdf/jemh104.pdf
- CBSE, Mathematics curriculum, Class X, 2026-27, page 4 (quadratic equations, real roots only): cbseacademic.nic.in/web_material/CurriculumMain27/SecPart1/Maths_SecP1X_2026-27.pdf
The definitions, the discriminant rule and the formula are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.