Question

Use a graphing calculator and a system of equations to find the roots of the equation.

x4 − 4x3 = 6x2 − 12x

From least to greatest, what are the integral roots of the equation?

Answer 1

First move all terms to one side:
x^4 − 4x^3 − 6x^2 + 12x = 0
Factor out x:
x(x^3 − 4x^2 − 6x + 12) = 0
So x = 0 or x^3 − 4x^2 − 6x + 12 = 0. Test integer roots; x = −2 works:
(x^3 − 4x^2 − 6x + 12) ÷ (x + 2) = x^2 − 6x + 6
Solve the quadratic: x = 3 ± √3 (not integers).

Thus the integral roots, least to greatest, are: −2, 0.