document.write( "Question 414332: one root of the quadratic equation x2-kx+8=0 is negative of the other. the value of k is \n" ); document.write( "

Algebra.Com's Answer #290620 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
one root of the quadratic equation x²-kx+8=0 is negative of the other. the value of k is\r
\n" ); document.write( "\n" ); document.write( "--------------------------------------
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "There are two ways to do this:\r\n" );
document.write( "\r\n" );
document.write( "First way:  Let the roots be +r and -r\r\n" );
document.write( "\r\n" );
document.write( "Then\r\n" );
document.write( "\r\n" );
document.write( "x² - kx + 8 = 0\r\n" );
document.write( "\r\n" );
document.write( "whould have to factor as\r\n" );
document.write( "\r\n" );
document.write( "(x - r)(x + r) = 0\r\n" );
document.write( "\r\n" );
document.write( "which multiplies out to\r\n" );
document.write( "\r\n" );
document.write( "x² + rx - rx + r² = 0\r\n" );
document.write( "\r\n" );
document.write( "          x² + r² = 0 \r\n" );
document.write( "\r\n" );
document.write( "So since the terms in x cancel, the coefficient of r\r\n" );
document.write( "must be zero, which makes k = 0.\r\n" );
document.write( "\r\n" );
document.write( "However the roots are imaginary since r² must equal to 8\r\n" );
document.write( "\r\n" );
document.write( "x² + 8 = 0\r\n" );
document.write( "\r\n" );
document.write( "    x² = -8\r\n" );
document.write( "           __ \r\n" );
document.write( "     x = ±Ö-8\r\n" );
document.write( "             ___\r\n" );
document.write( "     x = ± iÖ4*2\r\n" );
document.write( "             _\r\n" );
document.write( "     x = ±2iÖ2\r\n" );
document.write( "\r\n" );
document.write( "------------------------\r\n" );
document.write( "\r\n" );
document.write( "The other way to do it is to use the quadratic formula:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x² - kx + 8 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "               \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The two roots are \r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( "Setting one equal to the negative or the other:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 2\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtracting the radical from both sides:\r\n" );
document.write( "\r\n" );
document.write( "          k = -k\r\n" );
document.write( "\r\n" );
document.write( "         2k = 0\r\n" );
document.write( "\r\n" );
document.write( "          k = 0\r\n" );
document.write( "\r\n" );
document.write( "And the two roots are\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );