document.write( "Question 1187777: If x2 - tx + t = 0, where t > 0, has one solution for x, then x is equal to\r
\n" ); document.write( "\n" ); document.write( "A 1\r
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\n" ); document.write( "\n" ); document.write( "C - t + t2- t\r
\n" ); document.write( "\n" ); document.write( "D 2\r
\n" ); document.write( "\n" ); document.write( "E - t \n" ); document.write( "

Algebra.Com's Answer #818790 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "If x2 - tx + t = 0, where t > 0, has one solution for x, then x is equal to
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\n" ); document.write( "C) - t + t2- t
\n" ); document.write( "D) 2
\n" ); document.write( "E) - t
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document.write( "We are given the equation  x^2 - tx + t = 0,  where t > 0,\r\n" );
document.write( "and the problem asks to find its root x under the condition that this root is UNIQUE,\r\n" );
document.write( "which means that there is no other roots.\r\n" );
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document.write( "It is the case, when a quadratic equation has MERGING roots.\r\n" );
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document.write( "For it, the necessary and sufficient condition is d = 0, where  \" d \"  is the discriminant \r\n" );
document.write( "of the quadratic equation  d = (b^2 - 4ac).\r\n" );
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document.write( "In our case,  b = -t, a = 1, c = t, so the discriminant is  d = (-t)^2 - 4t = t^2 - 4t.\r\n" );
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document.write( "The discriminant is zero,  t^2-4t = 0 = t*(t-4),  if  \"t\" is  0  or  4.\r\n" );
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document.write( "The case  t= 0  is excluded by the condition, since t must be positive.\r\n" );
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document.write( "So,  t = 4  is the only possibility.\r\n" );
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document.write( "For t = 4 we have\r\n" );
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document.write( "    x^2 -4t + 4 = (x-2)^2,\r\n" );
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document.write( "and the only root of it is  x = 2.\r\n" );
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document.write( "ANSWER.  Under given conditions,  x = 2.\r\n" );
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