Theorems About Roots of Polynomial Equations

Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3 - x2 - x - 3 = 0. Do not find the actual roots.

-3, -1, 1, 3

Find the roots of the polynomial equation. 2x3 + 2x2 - 19x + 20 = 0

3+i/2, 3-i/2, - 4

A cubic polynomial with rational coefficients has the roots 6 +square root over 6 and 2/3. Find one additional root.

6- square root over 6

What does Descartes's Rule of Signs tell you about the real roots of the polynomial? -2x3 + 3x2 - 5x - 2 = 0

There are either 2 or 0 positive roots and one negative root.

Find a third-degree polynomial equation with rational coefficients that has roots -4 and 6 + i.

x3 - 8x2 - 11x + 148 = 0