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

1 Answer
Aug 19, 2015

Answer:

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.