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NCERT Class 10 Mathematics Exercise 2.2 Solutions: Polynomials
AI-written, checked on 23 Oct 2026
Solutions written by Shishya, checked — not the board's official answers
Step-by-step working for every question of Exercise 2.2 in NCERT's Class 10 Mathematics book, chapter “Polynomials”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.
How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.
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Ex 2.2 Q1
Find the zeroes and verify the relation between zeroes and coefficients: (i) x² − 2x − 8 (ii) 4s² − 4s + 1 (iii) 6x² − 3 − 7x (iv) 4u² + 8u (v) t² − 15 (vi) 3x² − x − 4.
- For ax² + bx + c the zeroes α, β satisfy α + β = −b/a and αβ = c/a; find the zeroes by factorising, then check both.
why?
For a quadratic polynomial ax² + bx + c, the sum of its zeroes is −b/a and their product is c/a.
- (i) x² − 2x − 8 = (x − 4)(x + 2), so the zeroes are 4 and −2. Sum = 2 = −(−2)/1; product = −8 = −8/1.
- (ii) 4s² − 4s + 1 = (2s − 1)², so both zeroes are 1/2. Sum = 1 = −(−4)/4; product = 1/4 = 1/4.
- (iii) Write it as 6x² − 7x − 3 = 6x² − 9x + 2x − 3 = 3x(2x − 3) + 1(2x − 3) = (3x + 1)(2x − 3), so the zeroes are −1/3 and 3/2.
- (iii) Sum = −1/3 + 3/2 = 7/6 = −(−7)/6; product = −1/2 = −3/6.
- (iv) 4u² + 8u = 4u(u + 2), so the zeroes are 0 and −2. Sum = −2 = −8/4; product = 0 = 0/4.
- (v) t² − 15 = (t − √15)(t + √15), so the zeroes are √15 and −√15. Sum = 0 = −0/1; product = −15 = −15/1.
- (vi) 3x² − x − 4 = 3x² − 4x + 3x − 4 = x(3x − 4) + 1(3x − 4) = (x + 1)(3x − 4), so the zeroes are −1 and 4/3.
- (vi) Sum = −1 + 4/3 = 1/3 = −(−1)/3; product = −4/3 = −4/3.
Answer: (i) −2, 4; (ii) 1/2, 1/2; (iii) −1/3, 3/2; (iv) −2, 0; (v) −√15, √15; (vi) −1, 4/3
- For ax² + bx + c the zeroes α, β satisfy α + β = −b/a and αβ = c/a; find the zeroes by factorising, then check both.
Ex 2.2 Q2
Find a quadratic polynomial whose sum and product of zeroes are: (i) 1/4, −1 (ii) √2, 1/3 (iii) 0, √5 (iv) 1, 1 (v) −1/4, 1/4 (vi) 4, 1.
- (i) The polynomial is k[x² − (sum)x + (product)], so k[x² − (1/4)x + (−1)].
- (i) Taking k = 4 to clear fractions gives 4x² − x − 4.
- (ii) The polynomial is k[x² − (√2)x + (1/3)].
- (ii) Taking k = 3 to clear fractions gives 3x² − 3√2x + 1.
- (iii) The polynomial is k[x² − (0)x + (√5)].
- (iii) Taking k = 1 gives x² + √5.
- (iv) The polynomial is k[x² − (1)x + (1)].
- (iv) Taking k = 1 gives x² − x + 1.
- (v) The polynomial is k[x² − (−1/4)x + (1/4)].
- (v) Taking k = 4 to clear fractions gives 4x² + x + 1.
- (vi) The polynomial is k[x² − (4)x + (1)].
- (vi) Taking k = 1 gives x² − 4x + 1.
Answer: (i) 4x² - x - 4; (ii) 3x² - 3√2x + 1; (iii) x² + √5; (iv) x² - x + 1; (v) 4x² + x + 1; (vi) x² - 4x + 1
Other exercises in this chapter
- Exercise 2.1 — 1 questions
← Polynomials: notes, practice and all exercises
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