SOLUTION: Find a quadratic equation with roots (4+i) and (4-i).

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Question 176376: Find a quadratic equation with roots (4+i) and (4-i).
Found 2 solutions by Mathtut, EMStelley:
Answer by Mathtut(3670) About Me  (Show Source):
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
If a is a root of a quadratic equation, that means that (x-a) is a factor of the equation. Thus, (4+i) being a root means that (x-(4+i)) is a factor. Similarly, that means that (x-(4-i)) is a factor. Thus, the equation is
y=%28x-%284%2Bi%29%29%28x-%284-i%29%29
So, we need to multiply out the right hand side in order to determine the equation.
y=x%5E2-%284-i%29x-%284%2Bi%29x%2B%284%2Bi%29%284-i%29
y=x%5E2-4x%2Bix-4x-ix%2B16-4i%2B4i-i%5E2
y=x%5E2-8x%2B16%2B1
y=x%5E2-8x%2B17