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Question
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 + 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`
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