Class 10 Mathematics — Chapter 4: Quadratic Equations
67 practice questions · 23 Easy · 23 Medium · 21 Hard
Practise Class 10 Mathematics Chapter 4, "Quadratic Equations", with 67 NCERT-aligned multiple-choice questions. The set is split into 23 Easy, 23 Medium and 21 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"Quadratic Equations" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Quadratic Equations, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 10 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 67.
Key concepts: Quadratic Equations (Class 10 Mathematics)
A quadratic equation has the form ax² + bx + c = 0 (a ≠ 0). This chapter finds its roots by factorisation or the quadratic formula, and uses the discriminant to judge the nature of the roots.
- Standard form
- ax² + bx + c = 0 with a ≠ 0. A root (solution) makes the left side equal 0.
- Factorisation method
- Split the middle term so the expression factors into two linear factors, then set each factor to 0.
- Quadratic formula
- When factorisation is hard, the roots come directly from a, b and c.
- Discriminant
- D = b² − 4ac decides the nature of the roots without solving the equation.
- Nature of roots
- D > 0 → two distinct real roots; D = 0 → two equal real roots; D < 0 → no real roots.
Key formulas — Quadratic Equations
💡 Exam tips for Quadratic Equations
- Always reduce the equation to ax² + bx + c = 0 before reading off a, b, c.
- If D < 0 there are no real roots — don't try to force a real answer.
Sample questions
Which of the following is a quadratic equation?
A quadratic equation has the form ax² + bx + c = 0, with a ≠ 0. Only (a) fits.
The sum of a number and its reciprocal is 10/3. The number is:
Let x + 1/x = 10/3 ⇒ 3x² − 10x + 3 = 0 ⇒ (3x − 1)(x − 3) = 0 ⇒ x = 3 or 1/3.
For what value of k does kx² − 4x + 4 = 0 have equal roots?
Equal roots ⇒ D = 0. b² − 4ac = 16 − 16k = 0 ⇒ k = 1.
Quadratic Equations — FAQs
What are the key concepts in Class 10 Mathematics Quadratic Equations?+
A quadratic equation has the form ax² + bx + c = 0 (a ≠ 0). This chapter finds its roots by factorisation or the quadratic formula, and uses the discriminant to judge the nature of the roots. Key ideas include Standard form, Factorisation method, Quadratic formula, Discriminant, Nature of roots.
What does Class 10 Mathematics Chapter 4 (Quadratic Equations) cover on XamBaaz?+
It covers 67 NCERT-aligned MCQs on "Quadratic Equations" — 23 Easy, 23 Medium and 21 Hard — each with a timed quiz and an instant explanation, suitable 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 (limited-time launch price), with no per-chapter charges.
How should I revise "Quadratic Equations" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
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