Maths Class 10 Chapter 2: Polynomials

Maths Class 10 Chapter 2: Polynomials


Important Concepts and Formulas

1.      Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials, respectively.

2.      A linear polynomial in x is of the form ax + b.

3.      A quadratic polynomial in x is of the form ax2 + bx + c, where a, b, c are the real numbers and a 0.

4.      A cubic polynomial in x is of the form ax3 + bx2 + cx + d, where a, b, c, d are the real numbers and a 0.

5.      The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x-axis.

6.      A linear polynomial can have at most 1 zero, a quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.

7.      If α and β are the zeroes of the quadratic polynomial ax2 + bx + c, then
α + β = -b/a   and     αβ = c/a.

8.      If α, β and γ are the zeroes of the quadratic polynomial ax2 + bx + c, then
α + β + γ = -b/a,       αβ + βγ + γα = c/a   and     αβγ = -d/a.

9.      The division algorithm states that for any polynomial p(x) and any non-zero polynomial g(x), there exists 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).

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