document.write( "Question 182933: Please I need help with: quintun was solving a quadestic equation in the form ax^2+bx+c=0 using the quadestic formula. He made the mistake, however, of switching a and c in the formula and and as a result he got answers that were 3 times the correct answer. Find the product of the roots of the quadratic equation \n" ); document.write( "

Algebra.Com's Answer #137373 by Edwin McCravy(20054) $\"\"$ $\"About$

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Please I need help with: quintun was solving a quadestic equation in the form ax^2+bx+c=0 using the quadestic formula. He made the mistake, however, of switching a and c in the formula and and as a result he got answers that were 3 times the correct answer. Find the product of the roots of the quadratic equation.
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document.write( "For any quadratic equation of the form\r\n" );
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document.write( "the product of the two roots is .\r\n" );
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document.write( "Suppose the two roots are  and \r\n" );
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document.write( "Then \r\n" );
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document.write( "When he switched  and  in the\r\n" );
document.write( "quadratic formula, he got the roots for\r\n" );
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document.write( "to be  and \r\n" );
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document.write( "So their product  is ,\r\n" );
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document.write( "and that had to equal the number \r\n" );
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document.write( "so \r\n" );
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document.write( "So we have the system:\r\n" );
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document.write( "Clearing of fractions:\r\n" );
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document.write( "Solving each for the product \r\n" );
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document.write( "So we have\r\n" );
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document.write( "cross-multiplying gives:\r\n" );
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document.write( "or\r\n" );
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document.write( "so, factoring,\r\n" );
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document.write( "So either  or \r\n" );
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document.write( "Now in the first case, substitution of\r\n" );
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document.write( "of  for  in \r\n" );
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document.write( "gives\r\n" );
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document.write( "In the second case, substitution of\r\n" );
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document.write( "of  for  in \r\n" );
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document.write( "gives\r\n" );
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document.write( "So the product of the roots is either\r\n" );
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document.write( " or \r\n" );
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document.write( "Those are the answers!\r\n" );
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document.write( "If you want to demonstrate those answers in\r\n" );
document.write( "specific cases, solve the quadratic equation:\r\n" );
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document.write( " and you'll find the solutions\r\n" );
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document.write( "and  and  which have \r\n" );
document.write( "product \r\n" );
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document.write( "Then switch  and  and you'll\r\n" );
document.write( "get the equation\r\n" );
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document.write( " and you'll find that it has\r\n" );
document.write( "solutions   and  which \r\n" );
document.write( "are 3 times the solutions  and .\r\n" );
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document.write( "Edwin

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