# If α And β Are the Zeros of the Quadratic Polynomial F(X) = Ax2 + Bx + C, Then Evaluate α4 + β4 - Mathematics

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4

#### Solution

f(x) = ax2 + bx + c

α + β = (-b/a)

αβ = c/a

since α + β are the roots (or) zeroes of the given polynomials

then

α4 + β= (α2 + β2)2 -2α2 + β2

= ((α + β)2 - 2αβ)2 - 2(αβ)2

=[(-b/a)^2-2c/a]^2-[2(c/a)^2]

=[(b^2-2ac)/a^2]^2-(2c^2)/a^2

=((b^2"2ac")^2-2a^2c^2)/a^4

Concept: Relationship Between Zeroes and Coefficients of a Polynomial
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Exercise 2.1 | Q 2.5 | Page 35