The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. What is $a+b$? Could you also explain how this is done? I'm kind of confused.

Guest Jan 20, 2020

edited by
Guest
Jan 20, 2020

#1**+1 **

One of doing this is to work backwards.

if the roots of an equation are p and q, then the equation is (z - p)(z - q) = 0.

So, if the roots are 2 - 3i and 2 + 3i, then the equation is [z - (2 - 3i)]·[z - (2 + 3i)] = 0

If you multiply out the left-hand side of that equation and combine like terms, you get z^{2} + 13 = 0

Since there is no z-term, the value of a is 0.

The value of b is 13.

geno3141 Jan 20, 2020