SOLUTION: write quadratic equation whose solutions are 1+2i and 1-2i The equation is x^2-_x+_=0

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Question 985919: write quadratic equation whose solutions are 1+2i and 1-2i
The equation is x^2-_x+_=0
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The sum of the roots is  (1+2i) + (1-2i) = 2.

The product of the roots is  (1+2i)*(1-2i) = 1 - %282i%29%5E2 = 1 - 4*(i^2) = 1 - 4*(-1) = 1+4 = 5.

Hence,  the quadratic equation is

(x-x1)*(x-x2) = 0,     or

x%5E2 - %28x1%2Bx2%29 + x1%2Ax2 = 0,     or

x%5E2 - 2x + 5 = 0.