Polynomials Notes: Class 10 Maths Chapter 2
Class 10 Maths Chapter 2 Polynomials covers the geometrical meaning of zeroes of a polynomial, the relationship between zeroes and coefficients, and division of polynomials.
Overview of Topics & Subtopics (Click to Jump)
1. Geometrical Meaning of the Zeroes of a Polynomial
Short Note:
• The zeroes of a polynomial p(x) are the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
• A linear polynomial has at most 1 zero, a quadratic has at most 2, and a cubic has at most 3 zeroes — in general, a polynomial of degree n has at most n zeroes.
2. Relationship between Zeroes and Coefficients
Short Note:
• For a quadratic polynomial ax² + bx + c with zeroes α and β: Sum of zeroes α + β = −b/a; Product of zeroes αβ = c/a.
• For a cubic polynomial ax³ + bx² + cx + d with zeroes α, β, γ: α+β+γ = −b/a; αβ+βγ+γα = c/a; αβγ = −d/a.
3. Division Algorithm for Polynomials
Short Note:
• If p(x) and g(x) are polynomials with g(x) ≠ 0, then there exist polynomials 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).
• This is used to check if one polynomial is a factor of another, or to find remaining zeroes when some zeroes are already known.