document.write( "Question 705199: 1. If $\"1%2F2\"$ is one of the roots of the quadratic equation $\"kx%5E2-2kx%2Bk-1=0\"$ , find the value of $\"k\"$ .\r
\n" ); document.write( "\n" ); document.write( "2. If $\"1%2Fm\"$ is one of the roots of the quadratic equation $\"mx%5E2%2B7x-2m=0\"$ , find the value of $\"m\"$ \n" ); document.write( "

Algebra.Com's Answer #434445 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
Choosing #1 and abbreviating the solution process,\r
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\n" ); document.write( "\n" ); document.write( "General solution to quadratic equation gives, after appropriate simplification steps, $\"x=%28k%2Bsqrt%28k%29%29%2Fk\"$ or $\"x=%28k-sqrt%28k%29%29%2Fk\"$ . Now since one of the roots is 1/2, we should equate 1/2 to this expression for x (both of them just to be thorough) and try solving for k. \r
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\n" ); document.write( "\n" ); document.write( " $\"1%2F2=%28k%2Bsqrt%28k%29%29%2Fk\"$ , and $\"1%2F2=%28k-sqrt%28k%29%29%2Fk\"$ .
\n" ); document.write( "Either way ultimately gives k^2-4k=0,
\n" ); document.write( " $\"k%28k-4%29=0\"$ ,
\n" ); document.write( "and since k=0 does not have any use here, we choose k=4. \r
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\n" ); document.write( "\n" ); document.write( "Our original quadratic equation could be amended for k=4 as,
\n" ); document.write( " $\"4x%5E2-2%2A4x%2B4-1=0\"$
\n" ); document.write( " $\"4x%5E2-8x%2B3=0\"$
\n" ); document.write( ".
\n" ); document.write( "...and if all was done well, one of the roots should be found to be 1/2
\n" ); document.write( "(but I did not yet actually check this). \n" ); document.write( "

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