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.

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

Step-by-step 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.