Chapter 2 — Polynomials

NCERT Class 10 Maths Chapter 2 covers Polynomials — their degrees, zeroes, geometrical meaning on graphs, and the relationship between zeroes and coefficients of quadratic and cubic polynomials.

Chapter 2 of NCERT Class 10 Mathematics introduces polynomials classified by degree: linear (degree 1), quadratic (degree 2), and cubic (degree 3). It explains zeroes of a polynomial as the x-coordinates where the graph of y = p(x) intersects the x-axis. A quadratic polynomial can have at most 2 zeroes and a cubic at most 3. The chapter derives key formulas linking zeroes to coefficients: for a quadratic ax² + bx + c, the sum of zeroes equals −b/a and the product equals c/a. For a cubic ax³ + bx² + cx + d, three analogous relationships connect the zeroes α, β, γ to a, b, c, and d.

1. 01Polynomials of degree 1, 2, and 3 are called linear, quadratic, and cubic polynomials respectively
2. 02A real number k is a zero of polynomial p(x) if p(k) = 0; geometrically, zeroes are x-coordinates where the graph y = p(x) crosses the x-axis
3. 03A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes
4. 04For a quadratic ax² + bx + c with zeroes α and β: sum of zeroes = −b/a and product of zeroes = c/a
5. 05For a cubic ax³ + bx² + cx + d with zeroes α, β, γ: α+β+γ = −b/a, αβ+βγ+γα = c/a, and αβγ = −d/a
6. 06The graph of a quadratic polynomial is a parabola that can intersect the x-axis at 0, 1, or 2 points, corresponding to 0, 1, or 2 zeroes