document.write( "Question 1074883: If two prime numbers are roots of the equation x^2-12x+k=0, what is the value of k? \n" ); document.write( "

Algebra.Com's Answer #689573 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The symmetry axis for this parabola is x = 6, for any value of k.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, for any value of k, the roots are equidistant from the point x = 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since we are looking for integer positive roots, we can have only these pairs:\r\n" );
document.write( "\r\n" );
document.write( "(5,7)\r\n" );
document.write( "\r\n" );
document.write( "(4,8)\r\n" );
document.write( "\r\n" );
document.write( "(3,9)\r\n" );
document.write( "\r\n" );
document.write( "(2,10)\r\n" );
document.write( "\r\n" );
document.write( "(1,11)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of them, only the pair (5,7) satisfies the given condition.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  Only the pair (5,7) satisfies the given condition, which gives k = 5*7 = 35.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );