SOLUTION: Can you help with this problem: Show that there is no quadratic equation ax^2 + bx + c = 0 such that a, b, and c are real numbers and 3i and -2i are solutions. Thanks for your

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Question 361774: Can you help with this problem: Show that there is no quadratic equation ax^2 + bx + c = 0 such that a, b, and c are real numbers and 3i and -2i are solutions.
Thanks for your help.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If 3i and -2i are solutions, then %28x-3i%29 and %28x%2B2i%29 are factors of the quadratic equation.
%28x-3i%29%28x%2B2i%29=ax%5E2%2Bbx%2Bc
x%5E2%2B2ix-3ix-6i%5E2=ax%5E2%2Bbx%2Bc
x%5E2%2B%28-3i%2B2i%29x%2B6=ax%5E2%2Bbx%2Bc
x%5E2-ix%2B6=ax%5E2%2Bbx%2Bc
Comparing
a=1
b=-i
c=6
However a,b, and c are supposed to be real.
Therefore 3i and -2i cannot be solutions where a,b, and c are real numbers.