Question

What can you say about the nature of any other zeros of the quadratic equation ax^2+bx+c=0 , which has one complex zero? Explain your answer.

Answer 1

The roots of a quadratic equation are given by :

$\frac{-b+ \sqrt{D} }{2a}$ and $\frac{-b- \sqrt{D} }{2a}$

so if one of these roots (zeros) is complex, it means that D<0.

This makes the other zero complex as well.

so if one of the roots is complex, the other is also complex, and these complex roots are the conjugates of each other.