Question

Find the equation whose roots are given by adding 2 to the roots of the equation

\[\large\rm x^4+3x^3-13x^2-51x-36=0 \ \]

Answer 1

Note:- We are not allowed to first solve the equation. The second equation should be given without solving the equation

Example
second coefficient = b/a = -Σa = -3
Since we are adding two to every root so
b/a = -(Σa +2) = -(Σa +Σ2) = -(-3+8) = -5
thus the equation should have x^4-5x³

Answer 2

@Evoker