Question

Find the zeros of the polynomial equation x³+2x²-11x-12=0 How many real zeros does this equation have?

Options:

A) 0 real zeros

B) 1 real zero

C) 2 real zeros

D) 3 real zeros

E) 4 real zeros

Answer 1

To find the zeros of the polynomial equation x³+2x²-11x-12=0, we can use the Rational Root Theorem and synthetic division. The possible rational roots are determined by the factors of the constant term, which in this case is 12. By using synthetic division with these possible roots, we find that -3 and 1 are the two real zeros of the equation.

Step-by-step explanation:

To find the zeros of the polynomial equation x³+2x²-11x-12=0, we can use the Rational Root Theorem and synthetic division. The possible rational roots are determined by the factors of the constant term, which in this case is 12. The factors of 12 are ±1, ±2, ±3, ±4, ±6, and ±12.

By using synthetic division with these possible roots, we find that -3 and 1 are the two real zeros of the equation. So the correct answer is C) 2 real zeros.