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 to both ends to get

x^2-2x+3 = 0

Multiply both sides by (x+2) to get:

0 = (x^2-2x+3)(x+2) = x^3-x+6

Add x-6 to both ends and transpose to get:

x^3 = x-6

So the roots of this cubic equation are x = -2 and the roots of x(2-x) = 3, including alpha.