Q1.GraphEasy · 1m
What do the zeroes of a polynomial represent on its graph?
Answer: The points where the graph of the polynomial intersects the x-axis.
Class 10 · Maths · Important Questions
Polynomials — Important Questions
Q2.Zeroes & CoefficientsEasy · 2m
Find the sum and product of the zeroes of x² − 5x + 6.
Answer: Sum = −b/a = 5; product = c/a = 6.
Q3.Forming a PolynomialMedium · 2m
Form a quadratic polynomial whose zeroes are 3 and −2.
Answer: x² − (sum)x + product = x² − (1)x + (−6) = x² − x − 6.
Q4.Finding ZeroesMedium · 3m
Find the zeroes of x² − 7x + 10 and verify the relation between zeroes and coefficients.
Answer: x² − 7x + 10 = (x − 2)(x − 5) ⇒ zeroes 2 and 5. Sum = 7 = −(−7)/1 ✓ and product = 10 = 10/1 ✓.
Q5.Division AlgorithmHard · 3m
State the division algorithm for polynomials.
Answer: For polynomials p(x) and g(x) with g(x) ≠ 0, there exist q(x) and r(x) such that p(x) = g(x)q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).
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