Fundamental Theorem of Algebra
A polynomial function has at least one zero in the set of complex numbers.
The Fundamental Theorem of Algebra states that "An nth degree polynomial function has exactly n zeros in the set of complex numbers, counting repeated zeros."
g(x) = x3 – 2x2 + 9x – 18
Set g(x) = 0 and factor over the complex numbers to find the zeros.
0 = x2(x – 2) + 9(x – 2)
0 = (x – 2)(x2 + 9)
0 = (x – 2)(x + 3i)(x – 3i)
x = 2 or x = –3i or x = 3i
The zeros of the function are 2, 3i, –3i
Note: The real numbers are a subset of the complex numbers because every real number can be written in a + bi form.