document.write( "Question 1209115: Wilma and Greg were trying to solve the quadratic equation
\n" ); document.write( "x^2 + bx + c = 0.
\n" ); document.write( "Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 5 and 15. Greg wrote down the wrong value of c (but his value of b was correct), and found the roots to be -5 and -7. What are the actual roots of x^2 + bx + c = 0? \n" ); document.write( "

Algebra.Com's Answer #847698 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "When the leading coefficient of a quadratic equation is 1, then,\r\n" );
document.write( "according to Vieta's theorem, the sum of the roots is the coefficient at x with the opposite sign,\r\n" );
document.write( "and the product of the roots is the constant term.\r\n" );
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document.write( "Wilma's roots 5 and 15 produce the correct constant term 5*15 = 75.\r\n" );
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document.write( "Greg's roots produce the correct coefficient at x  -(-5+(-7)) = -(-5-7) = -(-12) = 12.\r\n" );
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document.write( "So, the correct equation is\r\n" );
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document.write( "    x^2 + 12x + 75 = 0.\r\n" );
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document.write( "Its roots are complex numbers\r\n" );
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document.write( "     =  =  = .\r\n" );
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