If 3 + 2i is a solution for x^2 + bx + c = 0, where b and c are real numbers, then what are b and c?
If 3 + 2i is a root then so is 3 -2i
-b = the sum of the roots = 6
So b = - 6
And c = the product of the roots = (3 + 2i) ( 3 - 2i) = 9 - 4i^2 = 9 - 4 (-1) = 13
So the polynoimial is
x^2 - 6x + 13
