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…
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NCERT Solutions for Class 10 Mathematics — Quadratic Equations Exemplar. Step-by-step answers to all 5 textbook questions from this chapter, written for CBSE board preparation and free to use.
Quadratic Equations Exemplar — All 5 Questions Solved
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.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.