SOLUTION: Write a quadratic equation in vertex form whose has one root 1 + the square root of 3 over 3 i

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Question 175023: Write a quadratic equation in vertex form whose has one root 1 + the square root of 3 over 3 i
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex form is
y+=+a%28x-h%29%5E2+%2B+k where the vertex is at (h,k)
y+=+ax%5E2+-+2ahx+%2B+ah%5E2+%2B+k
y+=+x%5E2+-+2hx+%2B+h%5E2+%2B+k%2Fa
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Given that one of the roots is
%281+%2B+sqrt%283%29%29%2F3i
The other is
%281+-+sqrt%283%29%29%2F3i
If x%5B1%5D and x%5B2%5D are the roots

x%5E2+-+2%2F%283i%29x+%2B+2%2F9
h%5E2+%2B+k%2Fa+=+2%2F9
-2h+=+-2%2F%283i%29
h+=+1%2F%283i%29
h+=+-i%2F3
a+=+1
h%5E2+%2B+k%2Fa+=+2%2F9
%28-i%2F3%29%5E2+%2B+k+=+2%2F9
1%2F9+%2B+k+=+2%2F9
k+=+1%2F9
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The vertex form is
y+=+a%28x-h%29%5E2+%2B+k where the vertex is at (h,k)
y+=+%28x+%2B+%28i%2F3%29%29%5E2+%2B+1%2F9 answer
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+%282i%2F3%29%2Ax+%2B+4%2F9%29+
I think my method is OK, I
may have messed up the algebra