document.write( "Question 179376: An original quadratic equation for x is of the form: x^2+bx+c=0. If c is increased by 4, the roots for x of the resulting equation are equal, but if the original c is decreased by 5 one of the roots for x in this resulting equation is twice the other. Find the product of the roots for x in the original quadratic equation. \n" ); document.write( "

Algebra.Com's Answer #134305 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
If the roots are $\"r%5B1%5D\"$ and $\"r%5B2%5D\"$ , I can write
\n" ); document.write( " $\"%28x+-+r%5B1%5D%29%2A%28x+-+r%5B2%5D%29+=+0\"$
\n" ); document.write( " $\"x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29x+%2B+r%5B1%5D%2Ar%5B2%5D+=+0\"$
\n" ); document.write( "the original equation is of the form
\n" ); document.write( " $\"x%5E2+%2B+bx+%2B+c+=+0\"$
\n" ); document.write( " $\"c+=+r%5B1%5D%2Ar%5B2%5D\"$
\n" ); document.write( "(1) $\"c+%2B+4+=+%28r%5B1%5D%29%5E2\"$
\n" ); document.write( " $\"c+-+5+=+r%5B1%5D%2A%28r%5B1%5D%2F2%29\"$
\n" ); document.write( "(2) $\"2%2A%28c+-+5%29+=+%28r%5B1%5D%29%5E2\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( " $\"2c+-+10+-+c+-+4+=+0\"$
\n" ); document.write( " $\"c+=+14\"$
\n" ); document.write( "The product of the roots is 14
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"c+%2B+4+=+%28r%5B1%5D%29%5E2\"$
\n" ); document.write( " $\"18+=+%28r%5B1%5D%29%5E2\"$
\n" ); document.write( " $\"r%5B1%5D+=+sqrt%2818%29\"$
\n" ); document.write( " $\"r%5B1%5D+=+3%2Asqrt%282%29\"$
\n" ); document.write( " $\"c+=+r%5B1%5D%2Ar%5B2%5D\"$
\n" ); document.write( " $\"14+=+3%2Asqrt%282%29%2A+r%5B2%5D\"$
\n" ); document.write( " $\"r%5B2%5D+=+%2814%2Asqrt%282%29%29%2F6\"$
\n" ); document.write( " $\"r%5B1%5D%2Ar%5B2%5D+=+%283%2Asqrt%282%29%29%2A%2814%2Asqrt%282%29%29%2F6\"$
\n" ); document.write( " $\"r%5B1%5D%2Ar%5B2%5D+=+%2814%2A2%29%2F2\"$
\n" ); document.write( " $\"14+=+14\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );