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

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Question 187719: Find the quadratic equation with roots (4+i) and (4-i)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
x=4%2Bi or x=4-i Start with the given roots.


x-4=i or x-4=-i Get the real numbers to the left side.


%28x-4%29%5E2=%28i%29%5E2 or %28x-4%29%5E2=%28-i%29%5E2 Square both sides.


%28x-4%29%5E2=-1 or %28x-4%29%5E2=-1 Square "i" to get -1. Square "-i" to get -1.


Since these equations are identical, this means that we can use one equation


%28x-4%29%5E2=-1


x%5E2-8x%2B16=-1 FOIL the left side


x%5E2-8x%2B16%2B1=0 Add 1 to both sides.


x%5E2-8x%2B17=0 Combine like terms.



So the quadratic equation that has the roots 4+i and 4-i is y=x%5E2-8x%2B17