Question

if the equation 3x^3+2x^2+5x+7=0 has roots alpha,beta,gamma then the equation whose roots are alpha+2/alpha,beta+2/beta,gamma+2/gamma is

Answer 1

Answer:

Let a common root of roots of new equation be X.

So, here as alpha, beta, gamma are roots of equation formed by x, we take the values of alpha, beta, gamma as x.

So, x+(2/x) = X

on solving this, you get x = {X+√(X²-4)}/2

Now substitute this value in given old equation. Then, you get the new equation which has the given roots