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

4 roots.

EXPLANATION

The given polynomial function is

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.

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.