How many total roots must there be in this fourth-degree function? H(x)=4x^(4) -5x^(3)+2x^(2)-x+5

Question

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


`H(x)=4x^(4) -5x^(3)+2x^(2)-x+5`

Answer 1

It must have 4 roots

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