SOLUTION: Write a quadratic equation which has solutions of +- 7i

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Question 678441: Write a quadratic equation which has solutions of +- 7i
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If 7i and -7i are solutions then (x-7i) and (x-(-7i)) are factors. So we can start our equation with:
k(x-7i)(x-(-7i)) = 0
where "k" is any non-zero number. The last factor simplifies:
k(x-7i)(x+7i) = 0
Now we multiply the last two factors. We can use FOIL or the %28a-b%29%28a%2Bb%29+=+a%5E2-b%5E2 pattern. (I prefer using the pattern.)
k%28%28x%29%5E2+-+%287i%29%5E2%29+=+0
Simplifying...
k%28x%5E2+-+49i%5E2%29+=+0
Since i%5E2+=+-1:
k%28x%5E2+-+49%28-1%29%29+=+0
k%28x%5E2+%2B+49%29+=+0
Last of all, pick a value for k. It can be any non-zero number. (This is why the problem says "Write a equation..." instead of "Write the equation ...".) Picking a 1 for k makes things simple. Once you have your number for "k" just multiply out the left side using the Distributive Property.