Quadratic Equations Exemplar — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Quadratic Equations Exemplar" — 5 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Quadratic Equations Exemplar" — 5 important questions with detailed answers for CB…

By Syllab.in · Updated Jun 17, 2026

Key Questions Covered:

Solve 2x^2 - 7x + 3 = 0 using the quadratic formula.
Find nature of roots of x^2 - 6x + 9 = 0 without solving.
If α and β are roots of x^2 + 3x - 4 = 0, find α^2 + β^2.
A number exceeds its positive square root by 12. Find the number.
Solve 6x^2 - x - 1 = 0 by factorization.

Solutions Summary:

Question	Status
Solve 2x^2 - 7x + 3 = 0 using the quadratic formula.	✓ Solved
Find nature of roots of x^2 - 6x + 9 = 0 without solving.	✓ Solved
If α and β are roots of x^2 + 3x - 4 = 0, find α^2 + β^2.	✓ Solved
A number exceeds its positive square root by 12. Find the…	✓ Solved
Solve 6x^2 - x - 1 = 0 by factorization.	✓ Solved

Showing 5 of 5 questions

Q1: Solve 2x^2 - 7x + 3 = 0 using the quadratic formula.

a = 2, b = -7, c = 3. x = [7 ± √(49 - 24)]/4 = [7 ± √25]/4 = [7 ± 5]/4. So x = 12/4 = 3 or x = 2/4 = 1/2.

Q2: Find nature of roots of x^2 - 6x + 9 = 0 without solving.

Discriminant Δ = b^2 - 4ac = 36 - 36 = 0. Since Δ = 0, roots are real and equal.

Q3: If α and β are roots of x^2 + 3x - 4 = 0, find α^2 + β^2.

α + β = -3, αβ = -4. α^2 + β^2 = (α + β)^2 - 2αβ = 9 - 2(-4) = 9 + 8 = 17.

Q4: A number exceeds its positive square root by 12. Find the number.

Let number be x. Then x - √x = 12. Let √x = y, so y^2 - y - 12 = 0. Factoring: (y - 4)(y + 3) = 0. So y = 4 (taking positive). Thus x = 16.

Q5: Solve 6x^2 - x - 1 = 0 by factorization.

6x^2 - x - 1 = 6x^2 - 3x + 2x - 1 = 3x(2x - 1) + 1(2x - 1) = (3x + 1)(2x - 1) = 0. So x = -1/3 or x = 1/2.

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