If alpha is a root of x(2-x) = 3 then can you define a cubic equation with integer coefficients and roots including -2 and alpha ?
1 Answer
Feb 18, 2017
Yes
Explanation:
Given:
3 = x(2-x) = 2x-x^2
Add
x^2-2x+3 = 0
Multiply both sides by
0 = (x^2-2x+3)(x+2) = x^3-x+6
Add
x^3 = x-6
So the roots of this cubic equation are