# If (2 - 4i) is a solution to a polynomial equation, is the complex conjugate, 2 + 4i, also a solution?

Dec 8, 2015

If the polynomial has Real number coefficients, then the complex conjugate of an imaginary root is also a root.

#### Explanation:

So, if the coefficients are real numbers, then the answer is "yes.

If the coefficients are not known to be real, then the answer is "maybe yes, maybe no".
$x - \left(2 - 4 i\right) = 0$ has only one zero, namely $2 - 4 i$

$\left(x - \left(2 - 4 i\right)\right) \left(x - i\right) = 0$ has two solutions, $2 - 4 i$ and $i$.