document.write( "Question 1128224: If (sqrt 3 - 1) is a root of the equation 2x^2-2kx+4 = 0, then k equals... \n" ); document.write( "

Algebra.Com's Answer #744705 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The equation\r\n" );
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document.write( "    2x^2 - 2kx + 4 = 0 \r\n" );
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document.write( "is equivalent to  (after dividing both sides by 2)\r\n" );
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document.write( "    x^2 - kx + 2 = 0.      (1)\r\n" );
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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" );
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document.write( "Then, applying the Vieta's theorem, the other root of the equation (1) is\r\n" );
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document.write( "     = . =  =  = .\r\n" );
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document.write( "Thus we know BOTH ROOTS of the equation (1) (even without solving it explicitly (!) ). They are\r\n" );
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document.write( "      and  .\r\n" );
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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" );
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document.write( "    k =  +  = .\r\n" );
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document.write( "Answer.  k = .\r\n" );
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