document.write( "Question 1136677: The value of q for which the difference between the roots of the equation x^2-qx+8=0 is 2 are
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Algebra.Com's Answer #754490 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "I easily can guess:  the roots 2 and 4 gives the product of 8 (the constant term) and the difference of 2.\r\n" );
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document.write( "Their sum is 6, which should be \" q\", according to Vieta's theorem.\r\n" );
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document.write( "So, the answer is q = 6, based on my guessing.\r\n" );
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document.write( "Let's look what the Algebra solution will give us.\r\n" );
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document.write( "Let x and (x-2) are the roots.\r\n" );
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document.write( "Then their product is 8:\r\n" );
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document.write( "    x*(x-2) = 8\r\n" );
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document.write( "    x^2 - 2x - 8 = 0\r\n" );
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document.write( "    (x-4)*(x+2) = 0.\r\n" );
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document.write( "So, there are 2 roots:  x= 4  and  x= -2.\r\n" );
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document.write( "The value  x= 4  gives that two roots  4 and 2 which I guessed above, with the value  of q= 6.\r\n" );
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document.write( "The value x= -2 gives two roots  -2 and -4, with the value of q = -6.\r\n" );
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document.write( "So, the problem has two answers:  q= 6  and  q= -6.    (Third line of the answers' choice)\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus Algebra solution helped me to find 2 answers to the problem question: more than I could guess (!)\r
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