Question

If alpha and beta are the zeros of the quadratic polynomial F(x)=x²-px+q then find the value of alpha cube +beta cube

Answer 1

alpha+beta= -b/a = -(-p /1)= p/1
alpha.beta = c/a = q/1
so, alpha+beta cube = (alpha+beta)cube - 3alpha beta(alpha+beta)
                                  =(p/1)cube -3 q/1 (p/1)
                                 =p cube -3q²