Question

if alpha,beta and gamma are the given roots of x^3 - ax^2 + bx-c=0 find the equation with roots 1/alpha, 1/beta, 1/gamma


plz help ​

Answer 1

Answer:

We know that if (a) is a root of equation f(x) = 0, then x-a is one factor of the equation.

Similarly we need to understand that if the given equation has roots as alpha, beta and gamma it must satisfy the equation.

Moving to the question, we need to frame an equation whose roots are alpha+2, gamma + 2 and beta+2.

So alpha -2, beta -2 and gamma -2 will be one root of the equation. So

replace x by x-2 in the given equation.

a (x-2)^3 + b (x-2) + c = 0 is the required solution.

ax^3−6x^2+(b+12a)x−(c+2b+8a)=0