Question

How many total roots must there be in this fourth-degree function?

Answer 1

Answer:

It must have 4 roots

Step-by-step explanation:

Fundamental Theorem of Algebra

One polynomial of degree n will have exactly n roots. The degree of a polynomial is the highest exponent of its variable. Some of the roots could be real, some could be imaginary (complex). If n is odd, at least one of the roots is real.

The polynomial given in the question is

$H(x)=4x^{4} -5x^{3}+2x^{2}-x+5$

has a degree of 4 (the highest exponent of x). According to the Fundamental Theorem of Algebra, it must have 4 roots