Four roots of a polynomial are 2, 4+i, 5-3i, and -2i. Which number is NOT necessarily a root of the equation? -2
B) 5+3i
C) 2i
D) 4-i

Question

Four roots of a polynomial are 2, 4+i, 5-3i, and -2i. Which number is NOT necessarily a root of the equation? -2
B) 5+3i
C) 2i
D) 4-i

terenzreignz · Answer

There is something you should know about complex roots of a polynomial (with real coefficients, of course)

If a complex number $\Large \color{red}a + \color{blue}bi$ is a root, then automatically (or necessarily) its CONJUGATE $\Large \color{red}a - \color{blue}bi$ is also a root of said polynomial ^_^