We want to state the total number of complexzeros for the given function. First, we need to write the function in the standard form.
f(x) = x^2-3x^5+4x-x^7-44
⇕
f(x) = - x^7 -3x^5+x^2-44
Now, we shall consider the complex roots. Let's recall the Fundamental Theorem of Algebra.
IfP(x) is a polynomial of degreen≥ 1,
thenP(x)=0 has exactlyn roots.
Those roots can be either real or imaginary. Both real and imaginary numbers are complex numbers. The polynomial in the given equation has a degree of 7. Thus, the equation has exactly seven complex roots.
