- #1
Faiq
- 348
- 16
Homework Statement
Find the equation whose roots are given by adding 2 to the roots of the equation
x^4+3x^3-13x^2-51x-36=0
Homework Equations
x^4-(Σa)x³+(Σab)x²-(Σabc)x+abcd = 0
The Attempt at a Solution
And the coefficient of x^3 to be -5
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
And I am stuck at x^2
=Σ(a+2)(b+2)
=Σab+2a+2b+4
=Σab+ 4Σa +16 which amounts to -9
Correct coefficient is -7
Note:- We aren't allowed to solve the given equation in any part of the working