Question 116013: Find a quadratic equation with roots (4 + i) and (4 - i).
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find a quadratic equation with roots (4 + i) and (4 - i).
:
It's kind of like the completing the square in reverse:
x = 4 +/-i
:
x - 4 = +/i
:
(x-4)^2 = i^2
which is
(x+4)^2 = -1
:
FOIL
x^2 - 8x + 16 = -1
:
x^2 - 8x + 16 + 1 = 0
:
x^2 - 8x + 17 = 0 is the quadratic equation
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