Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have?

x(x2 - 4)(x2 + 16) = 0 has __ complex roots

(x 2 + 4)(x + 5)2 = 0 has __ complex roots

x6 - 4x5 - 24x2 + 10x - 3 = 0 has __ complex roots

x7 + 128 = 0 has __ complex roots

(x3 + 9)(x2 - 4) = 0 has __ imaginary complex roots

Question

Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have?

x(x2 - 4)(x2 + 16) = 0 has __ complex roots

(x 2 + 4)(x + 5)2 = 0 has __ complex roots

x6 - 4x5 - 24x2 + 10x - 3 = 0 has __ complex roots

x7 + 128 = 0 has __ complex roots

(x3 + 9)(x2 - 4) = 0 has __ imaginary complex roots

thomasfire55 · Answer

@Jadeishere

jadeishere · Answer

@agent0smith 
He's going to be the guy to help. I know how to do this in my head, but not on paper or how to explain it xD

thomasfire55 · Answer

@agent0smith

agent0smith · Answer

Just work out the degree - the highest power of x. That's what you need.