document.write( "Question 678441: Write a quadratic equation which has solutions of +- 7i \n" ); document.write( "

Algebra.Com's Answer #421392 by jsmallt9(3758) $\"\"$ $\"About$

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:
\n" ); document.write( "k(x-7i)(x-(-7i)) = 0
\n" ); document.write( "where \"k\" is any non-zero number. The last factor simplifies:
\n" ); document.write( "k(x-7i)(x+7i) = 0
\n" ); document.write( "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.)
\n" ); document.write( " $\"k%28%28x%29%5E2+-+%287i%29%5E2%29+=+0\"$
\n" ); document.write( "Simplifying...
\n" ); document.write( " $\"k%28x%5E2+-+49i%5E2%29+=+0\"$
\n" ); document.write( "Since $\"i%5E2+=+-1\"$ :
\n" ); document.write( " $\"k%28x%5E2+-+49%28-1%29%29+=+0\"$
\n" ); document.write( " $\"k%28x%5E2+%2B+49%29+=+0\"$
\n" ); document.write( "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. \n" ); document.write( "

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