Question 120151: A quadratic equation has roots 1+-2i.What is the equation?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A quadratic equation has roots 1+-2i.What is the equation?
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Sort of like completing the square in reverse:
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x = 1 +/- 2i
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x - 1 = +/- 2i; subtract 1 from both sides
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(x-1)^2 = (+/-2i)^2; square both sides
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x^2 - 2x + 1 = 4(i^2); FOIL the left side
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x^2 - 2x + 1 = 4(-1); i^2 = -1
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x^2 - 2x + 1 = -4
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x^2 - 2x + 1 + 4 = 0; add 4 to both sides
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x^2 - 2x + 5 = 0; is the quadratic equation
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You can check this by completing the square, and see if you get the given roots
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