Question

Jamison graphs the function ƒ(x) = x4 − x3 − 19x2 − x − 20 and sees two zeros: −4 and 5. Since this is a polynomial of degree 4 and he only sees two zeros, he determines that the Fundamental Theorem of Algebra does not apply to this equation. Is Jamison correct? Why or why not?

Answer 1

Answer:

Jamison is not correct

Step-by-step explanation:

According to the Fundamental Theorem of Algebra, an nth degree polynomial has n roots.

These roots comprises of real roots and imaginary roots.

The given function is

$f(x) = {x}^{4} - {x}^{3} - 19 {x}^{2} - x - 20$

Based on the Fundamental Theorem of Algebra, this function should have four roots.

The graph of the function only reveals real zeros and not the imaginary zeros.

So aside −4 and 5, there are two complex zeros