Question

if alpha and beta are the zeros of the polynomial f(x)=ax2+bx+c then evaluate : a(alpha2/beta+beta 2/alpha) + b(alpha/beta+beta/alpha)

Answer 1

Answer:

If alpha,beta are roots of a quadratic equation ax^2+bx+c=0,then

alpha+beta=-b/a

alpha*beta=c/a

Therefore,alpha sq.+beta sq. =(alpha+beta)^2-2.alpha.beta

                                       =(-b/a)^2-2*c/a

                                       =b^2/a^2-2c/a