POLYNOMIALS

Class 10 Maths Formulas

CHAPTER 2 POLYNOMIALS
1.	x is a variable and a₀, a₁, a₂, … aₙ are real numbers, n is a positive integer. f(x) = a₀ + a₁x + a₂x² + … + aₙxⁿ is a polynomial in x.
2.	The exponent of the highest degree term is called the degree of the polynomial.
3.	Constant Polynomial: f(x) = a, where a is constant.
	Linear Polynomial: f(x) = ax + b, a ≠ 0 Quadratic Polynomial: f(x) = ax² + bx + c, a ≠ 0 Cubic Polynomial: f(x) = ax³ + bx² + cx + d, a ≠ 0
4.	A real number a is a zero of the polynomial f(x) if f(a) = 0.
5.	A polynomial of degree n can have at most n real zeros.
6.	Geometrically, the zeros of the polynomial f(x) are the x-coordinates where y = f(x) intersects the x-axis.
7.	If α and β are the zeroes of f(x) = ax² + bx + c, then:
	Sum of the Zeroes: α + β = −b/a Product of the Zeroes: αβ = c/a
8.	If sum and product of zeroes are given, then the quadratic polynomial is: k[x² − x(sum of zeroes) + (product of zeroes)] k[x² − x(α + β) + αβ]
9.	If α + β and αβ are known: α² + β² = (α + β)² − 2αβ α³ + β³ = (α + β)³ − 3αβ(α + β) α⁴ + β⁴ = (α² + β²)² − 2(αβ)²
10.	If α, β, γ are the zeroes of the cubic polynomial f(x) = ax³ + bx² + cx + d, then: α + β + γ = −b/a αβ + βγ + γα = c/a αβγ = −d/a