Question

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

Answer 1

The function `f(x)=x^12+x^9+x^7−2x^2` has `color(red)("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+bi`.

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.