SOLUTION: If b and c are real numbers so that the polynomial x^2+bx+c has 3+i as a zero, what is the value of b+c?

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Question 973676: If b and c are real numbers so that the polynomial x^2+bx+c has 3+i as a zero, what is the value of b+c?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Complex zeros of quadratic equations are in conjugate pairs.

%28x-%283%2Bi%29%29%28x-%283-i%29%29=x%5E2%2Bbx%2Bc
%28x-3-i%29%28x-3%2Bi%29
%28%28x-3%29-i%29%28%28x-3%29%2Bi%29
%28x-3%29%5E2-i%5E2
x%5E2-6x%2B9-%28-1%29
x%5E2-6x%2B9%2B1
x%5E2-6x%2B10=x%5E2%2Bbx%2Bc

Corresponding positions show b=-6 and c=10.

b%2Bc
-6%2B10
highlight%28highlight%284%29%29