# How many complex zeros does the function f(x) = x^12 + x^9 + x^7 - 2x^2 have?

Aug 19, 2015

The function f(x)=x^12+x^9+x^7−2x^2 has $\textcolor{red}{\text{12 complex zeroes}}$.

#### Explanation:

 f(x)=x^12+x^9+x^7−2x^2

According to the fundamental theorem of algebra, every polynomial of degree $n$ has $n$ complex zeroes.

Your function is a 12th degree polynomial, so it has twelve complex zeroes.

Note: a complex number is a number of the form $a + b i$.

If $b = 0$, then the number is real (the complex numbers include the real numbers).

If b≠0, then the number is imaginary.

If $a = 0$ and b≠0, then the number is pure imaginary.

The 12 complex zeroes of your function include four real zeroes and eight imaginary zeroes.