document.write( "Question 173400: The equation $\"x%5E2-3x-2=0\"$ has roots $\"alpha\"$ and $\"beta\"$ , and the equation $\"x%5E2-6x%2Bp=0\"$ has roots $\"k%2Falpha\"$ and $\"k%2Fbeta\"$ . find the value of $\"k\"$ and of $\"p\"$ . \n" ); document.write( "

Algebra.Com's Answer #128251 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
The equation $\"x%5E2-3x-2=0\"$ has roots $\"alpha\"$ and $\"beta\"$ , and the equation $\"x%5E2-6x%2Bp=0\"$ has roots $\"k%2Falpha\"$ and $\"k%2Fbeta\"$ . find the value of $\"k\"$ and of $\"p\"$ .
\n" ); document.write( "

\r\n" );
document.write( "We need to know two things about a quadratic equation of the\r\n" );
document.write( "form \r\n" );
document.write( "\r\n" );
document.write( "1.   the sum of the two roots with the sign changed.\r\n" );
document.write( "\r\n" );
document.write( "2.   the product of the two roots.\r\n" );
document.write( "\r\n" );
document.write( "We use 1 and 2 on the first equation:\r\n" );
document.write( "\r\n" );
document.write( "Since  has roots  and ,\r\n" );
document.write( "\r\n" );
document.write( "Using 1,  \r\n" );
document.write( "multiplying both sides by \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using 2,  \r\n" );
document.write( "\r\n" );
document.write( "Now we use 1 and 2 on the second equations:\r\n" );
document.write( "\r\n" );
document.write( "Since  has roots  and . \r\n" );
document.write( "\r\n" );
document.write( "Using 1,  \r\n" );
document.write( "multiplying both sides by \r\n" );
document.write( "\r\n" );
document.write( "getting the LCD of \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Combine numerators over the LCD:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor out  on top:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now,\r\n" );
document.write( "\r\n" );
document.write( "since we have above that ,\r\n" );
document.write( "and since , we can replace\r\n" );
document.write( " by ,\r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "since we have above that ,\r\n" );
document.write( "we can replace  by -2,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the value of  is \r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "Using 2 on the second equation, \r\n" );
document.write( " \r\n" );
document.write( "But since ,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now since from above, we have ,\r\n" );
document.write( "\r\n" );
document.write( " becomes\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the value of  is \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );