Question

According to the fundamental theorem of algebra, how many roots does the polynomial f(x)=x4+3x2+7 have over the complex numbers, and counting roots with multiplicity greater than one as distinct? (i.e f(x)=x2 has two roots, both are zero).

Answer 1

ANSWER

4 roots.

EXPLANATION

The given polynomial function is

$f(x) = {x}^{4} + 3 {x}^{2} + 7$

This is a fourth degree polynomial.

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

This roots include both real and complex roots.

Also repeated roots or roots with multiplicity greater than one are counted as distinct.

Since the given polynomial function is a fourth degree polynomial, the Fundamental Theorem of Algebra, says that this polynomial has 4 roots.