document.write( "Question 1094973: if the sum of the roots of 2x^2 -3cx + 2x +c^2 = 0 equals the product of roots, what are the possible values of c \n" ); document.write( "

Algebra.Com's Answer #709680 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "if the sum of the roots of 2x^2 -3cx + 2x +c^2 = 0 equals the product of roots, what are the possible values of c
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document.write( "Let me re-write the given equation in an equivalent form\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Then, according to Vieta's theorem, \r\n" );
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document.write( "    - the sum of the roots is equal to   = the coefficient at \"x\" taken with the opposite sign and divided by the leading coefficient,   \r\n" );
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document.write( "and\r\n" );
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document.write( "    - the product of the roots is equal to  = the constant term divided by the leading coefficient.\r\n" );
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document.write( "Therefore, the condition says and directly required that\r\n" );
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document.write( "     = ,   or, equivalently,\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "After factoring left side  c^2 - 3c + 2 = (c-1)*(c-2)  you easily find the roots  c= 1  and  c= 2.\r\n" );
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document.write( "Answer.  The values of \"c\" under the question are  c= 1  and  c= 2.\r\n" );
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