Quadratic Equations — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 4
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 4, "Quadratic Equations". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Quadratic Equations", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Quadratic Equations, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Quadratic Equations (Class 10 Mathematics)
A quadratic equation can have two, one or no real roots, and the discriminant decides which without solving. This chapter solves quadratics by factorisation, by completing the square and by the quadratic formula, and applies them to word problems.
- Quadratic equation
- An equation of the form ax² + bx + c = 0 with a ≠ 0. The condition a ≠ 0 is what keeps it quadratic rather than linear.
- Standard form
- Every quadratic must be rearranged to ax² + bx + c = 0 before any method is applied, with all terms on one side.
- Root of a quadratic
- A value of x satisfying the equation; geometrically it is where the parabola meets the x-axis.
- Solving by factorisation
- Split the middle term into two parts whose product is ac and whose sum is b, factor in pairs, then set each factor to zero.
Quadratic Equations — important questions & MCQs with answers (Class 10 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Which of the following is a quadratic equation?
A.x² + 2x − 3 = 0✓ CorrectB.2x − 5 = 0C.x³ − 1 = 0D.x⁴ + 2 = 0Answer: A. x² + 2x − 3 = 0
Explanation: A quadratic equation has degree exactly 2, form ax² + bx + c = 0 with a ≠ 0; 2x − 5 = 0 is linear, x³ − 1 = 0 cubic, x⁴ + 2 = 0 quartic — only x² + 2x − 3 = 0 fits the degree-2 pattern.
- Q2Easy
The roots of x² − 5x + 6 = 0 are:
A.−1, −6B.−2, −3C.1, 6D.2, 3✓ CorrectAnswer: D. 2, 3
Explanation: Factorise: x² − 5x + 6 = (x − 2)(x − 3) = 0, giving roots 2 and 3 — check: sum 5 matches −b/a and product 6 matches c/a.
- Q3Easy
The discriminant of x² − 4x + 4 = 0 is:
A.16B.4C.0✓ CorrectD.−4Answer: C. 0
Explanation: Discriminant D = b² − 4ac = (−4)² − 4(1)(4) = 16 − 16 = 0, so x² − 4x + 4 = 0 has equal real roots.
- Q4Easy
The roots of x² − 5x + 6 = 0 are:
A.3 and −2B.1 and 6C.−2 and −3D.2 and 3✓ CorrectAnswer: D. 2 and 3
Explanation: Factorise x² − 5x + 6 as (x − 2)(x − 3) = 0, giving roots x = 2 and x = 3.
- Q5Easy
The discriminant of ax² + bx + c = 0 is:
A.4ac − b²B.b² + 4acC.b² − 4ac✓ CorrectD.2aAnswer: C. b² − 4ac
Explanation: The discriminant of ax² + bx + c = 0 is defined as D = b² − 4ac; its sign tells you whether the roots are real or not.
- Q6Easy
For ax² + bx + c = 0 (a ≠ 0), the sum of roots is:
A.−b/a✓ CorrectB.b/aC.c/aD.−c/aAnswer: A. −b/a
Explanation: For ax² + bx + c = 0, Vieta's relations give the sum of roots as α + β = −b/a.
- Q7Medium
If one root of x² + kx + 12 = 0 is 4, then k =
A.4B.7C.−4D.−7✓ CorrectAnswer: D. −7
Explanation: Since x = 4 is a root, substitute: 4² + 4k + 12 = 0 → 16 + 4k + 12 = 0 → 4k = −28 → k = −7.
- Q8Medium
The nature of roots of 2x² − 3x + 5 = 0 is:
A.Not real✓ CorrectB.Real and equalC.Real and distinctD.Cannot be determinedAnswer: A. Not real
Explanation: D = b² − 4ac = (−3)² − 4(2)(5) = 9 − 40 = −31, which is negative, so the roots are not real.
- Q9Medium
Solve: 2x² + x − 6 = 0.
A.x = −2, −3B.x = −3/2, 2C.x = 2, 3D.x = 3/2, −2✓ CorrectAnswer: D. x = 3/2, −2
Explanation: Factorise 2x² + x − 6 = (2x − 3)(x + 2) = 0, giving x = 3/2 or x = −2 — split the middle term as 4x − 3x to match ac = −12.
- Q10Medium
For what value of k are roots of x² − kx + 9 = 0 equal?
A.−6B.6C.±6✓ CorrectD.3Answer: C. ±6
Explanation: Equal roots need D = 0: (−k)² − 4(1)(9) = k² − 36 = 0, so k² = 36 and k = ±6 — both signs work since k is squared.
- Q11Medium
A quadratic equation with roots 3 + √2 and 3 − √2 is:
A.x² − 6x − 7 = 0B.x² + 6x + 7 = 0C.x² − 6x + 7 = 0✓ CorrectD.x² − 6x + 11 = 0Answer: C. x² − 6x + 7 = 0
Explanation: Sum = (3+√2) + (3−√2) = 6, product = (3+√2)(3−√2) = 9 − 2 = 7, so the equation is x² − 6x + 7 = 0.
- Q12Hard
The product of a positive integer and the integer that is 5 less than it is 14. The integer is:
A.5B.7✓ CorrectC.6D.9Answer: B. 7
Explanation: x(x − 5) = 14 → x² − 5x − 14 = 0 → (x − 7)(x + 2) = 0, so x = 7 or −2; the positive integer is 7.
- Q13Hard
For what value of k does kx² − 4x + 4 = 0 have equal roots?
A.1✓ CorrectB.2C.−1D.0Answer: A. 1
Explanation: Equal roots need D = 0: (−4)² − 4(k)(4) = 16 − 16k = 0, so k = 1.
- Q14Hard
The quadratic equation 2x² + kx + 2 = 0 has equal roots when k equals:
A.±2B.±4✓ CorrectC.±√2D.±2√2Answer: B. ±4
Explanation: Equal roots need D = 0: k² − 4(2)(2) = k² − 16 = 0, so k = ±4.
Start this chapter free
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Start this chapter free →Quadratic Equations — FAQs
What are the key concepts in Class 10 Mathematics Quadratic Equations?+
A quadratic equation can have two, one or no real roots, and the discriminant decides which without solving. This chapter solves quadratics by factorisation, by completing the square and by the quadratic formula, and applies them to word problems. Key ideas include Quadratic equation, Standard form, Root of a quadratic, Solving by factorisation.
What does Class 10 Mathematics Chapter 4 (Quadratic Equations) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Quadratic Equations": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Quadratic Equations" questions free to practise?+
Yes. Sign in with Google to practise "Quadratic Equations" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Quadratic Equations" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Quadratic Equations" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Quadratic Equations" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Quadratic Equations (Class 10 Mathematics)?+
The questions that matter most test Quadratic equation, Standard form, Root of a quadratic, Solving by factorisation. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Quadratic Equations?+
Yes — Class 10 Mathematics Quadratic Equations has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.