Question

Using rational root theorem which of the following are possible roots X^4+8x^3-30x-72

Answer 1

A. 8

B. 12

Step-by-step explanation:

The rational root theorem says that the possible roots of the polynomial are fraction a/b where a is a divisor of the constant term and b is a divisor of the leading coefficient.

Since the equation is

x⁴ + 8x³ +13x² - 30x - 72

The constant term is -72 and the leading term is x⁴, so the leading coefficient is 1. The divisor of 1 is 1, so by the rational root theorem, the possible roots are the factors if 72.

Then, the factors of 72 are

1, 2, 4, 6, 8, 9, 12, 18, 36, 72

Therefore, the answers are

A. 8

B. 12