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​Q. ax^3 + bx^2 + cx + d=0 has 3 real roots alpha beta and gamma Find: alpha^4 + beta^4 + gamma^4 alpha ^5 + beta ^5 + gamma^5

​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

Grade:11

2 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago

We have newtons formula which says:
221-1538_gif.latex.gif

In your case divide the polynomial by a
then apply the newstons formulae.
Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago
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


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