document.write( "Question 175023: Write a quadratic equation in vertex form whose has one root 1 + the square root of 3 over 3 i \n" ); document.write( "

Algebra.Com's Answer #130123 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The vertex form is
\n" ); document.write( " $\"y+=+a%28x-h%29%5E2+%2B+k\"$ where the vertex is at (h,k)
\n" ); document.write( " $\"y+=+ax%5E2+-+2ahx+%2B+ah%5E2+%2B+k\"$
\n" ); document.write( " $\"y+=+x%5E2+-+2hx+%2B+h%5E2+%2B+k%2Fa\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Given that one of the roots is
\n" ); document.write( " $\"%281+%2B+sqrt%283%29%29%2F3i\"$
\n" ); document.write( "The other is
\n" ); document.write( " $\"%281+-+sqrt%283%29%29%2F3i\"$
\n" ); document.write( "If $\"x%5B1%5D\"$ and $\"x%5B2%5D\"$ are the roots
\n" ); document.write( "

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

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