Question

if alpha and beta are the zeroes of the quadritic polynomial f(t)=t^2-4t+3, find the value of alpha^4beta^3+alpha^3beta^4

Answer 1

The expression can be written as (t-1)×(t-3)

therefore zeroes of the equation are 1&3


Let alpha=1 & Beta=3

So alpha^4beta^3+alpha^3beta^4 =
(1^4×3^3)+(1^3×3^4)


Which is....27+81=108

Therefore final answer is 108

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