Question

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

Answer 1

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 + β⁴ = (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`