Question

The roots of the quadratic equation $z^2 + bz + c = 0$ are $5 + 3i$ and $5 - 3i$. What is $b+c$?

Answer 1

If the roots are 5 ± 3i, the quadratic is (z − (5+3i))(z − (5−3i)) = z^2 − 10z + 34. Thus b = −10 and c = 34, so b + c = 24.