Question

Three roots of the polynomial equation x - 4x3 - 2x2 + 12x + 9 = 0 are 3, -1 and -1. Explain why the fourth root must be a

real number. Find the fourth root.

Answer 1

The root must be -3 and be a real number.

Explanation:

Since the roots are 3, -1, -1 and x that means the equation can be converted into a(bx-3)(cx+1)(dx+e). -3 * 1 * e = 9. This means that e = -3. Since -3 belongs to the reals, that must mean the last root must be a real number.