​Q. ax^3 + bx^2 + cx + d=0 has 3 real roots alpha beta and gamma

Find:

1. alpha^4 + beta^4 + gamma^4
2. alpha ^5 + beta ^5 + gamma^5

We have newtons formula which says:


In your case divide the polynomial by a
then apply the newstons formulae.

the sum of roots is, alpha+beta+gamma = b/a
produc of roots is = d/a

alphabeta+ alphagamma+betagamma= -b/a

(alpha+beta+gamma)^2=alpha2+beta2+gamma2+alphabeta+ 2alphagamma+2betagamma

(alpha+beta+gamma)^4=(alpha2+beta2+gamma2+alphabeta+ 2alphagamma+2betagamma)^2