Question

According to the fundamental theorem of algebra, how many zeros does the function f(x) = 15x12 + 41x9 + 13x2 − 10 have?

Answer 1

According to the fundamental theorem of algebra, the function f(x) = 15x¹² + 41x⁹ + 13x² − 10 have 12 zeros.

Fundamental Theorem of Algebra states that "any polynomial of degree n has n roots, but we may need to use complex numbers".

The degree that we need to identify in a polynomial is the largest exponent used in the equation. In this case, 15x¹², has the largest exponent. It is the degree of n used to determine the number of zeros. Thus, n = 12 so number of zero is also 12.