Question

If alpha and beta are the zeros of the quadratic polynomial f(x):- a*x^2+b*x+c then evaluate alpha^4+ beta ^4

Answer 1

alpha^4+beta^4=(alpha^2+beta^2)^2 - 2(alpha beta)^2
                         =((alpha +beta)^2-2alphabeta)^2 - 2(alpha beta)^2
BUT ALPHA+BETA=-b/a
AND ALPHA BETA=c/a
so,
((b/a)^2-2(c/a))^2-2(c/a)^2 

Answer 2

alpha^4+beta^4=(alpha^2+beta^2)^2 - 2(alpha beta)^2
=((alpha +beta)^2-2alphabeta)^2 - 2(alpha beta)^2
BUT ALPHA+BETA=-b/a
AND ALPHA BETA=c/a
((b/a)^2-2(c/a))^2-2(c/a)^2