document.write( "Question 1128329: If (√3 - 1) is a root of the equation 2x^2-2kx+4 = 0, then k equals...
\n" ); document.write( "A)2√3-1 B)√3-2 C)2√3 D)√3 E)√3-1 \n" ); document.write( "

Algebra.Com's Answer #744901 by ikleyn(52787) $\"\"$ $\"About$

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

\r\n" );
document.write( "The equation\r\n" );
document.write( "\r\n" );
document.write( "    2x^2 - 2kx + 4 = 0 \r\n" );
document.write( "\r\n" );
document.write( "is equivalent to  (after dividing both sides by 2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - kx + 2 = 0.      (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We are given that    is the root of the original equation; hence, the equation (1) with the leading coefficient 1 has this root, too.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then, applying the Vieta's theorem, the other root of the equation (1) is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = . =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus we know BOTH ROOTS of the equation (1) (even without solving it explicitly (!) ). They are\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      and  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Again, according to Vieta's theorem, the sum of these roots is the coefficient at x in equation (1) taken with the opposite sign:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    k =  +  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  k = .\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved. // Option C).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );