Question

if 2+3i is one root of a quadratic equation with real coefficients, what is the sum of the roots of the equation?

Answer 1

Complex roots of any polynomial always come in conjugate pairs, such as a+bi and a-bi.

In the case of a quadratic there are only two roots and since in this case one is 2+3i the the other must be 2-3i.

So the sum of the roots is (2+3i)+(2-3i) = 4

we get the 4 from:

(2+3i)+(2-3i)
2+2+3i-3i
4 + 0
4