document.write( "Question 1156971: Find the ordered pair (a,b) of real numbers for which $\"x%5E2%2Bax%2Bb\"$ has a non-real root whose cube is 343. \n" ); document.write( "

Algebra.Com's Answer #779760 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "First we want a cubic equation whose three roots are the three cube roots of 343.\r\n" );
document.write( "We know that since 7³=343, that the REAL cube root of 343 is 7.  So the cubic\r\n" );
document.write( "equation we are looking for to begin with is:\r\n" );
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document.write( "                             x³ = 343\r\n" );
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document.write( "whose roots are the three cube roots of 343, which are the real root 7, and the\r\n" );
document.write( "two non-real cube roots of 343.  Get 0 on the right\r\n" );
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document.write( "                       x³ - 343 = 0\r\n" );
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document.write( "Factor:   (x - 7)(x² + 7x + 49) = 0\r\n" );
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document.write( "Use zero-factor property:\r\n" );
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document.write( "       x - 7 = 0;  x² + 7x + 49 = 0\r\n" );
document.write( "           x = 7;  \r\n" );
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document.write( "So x² + 7x + 49 = 0 has a non-real root whose cube is 343. In fact it has\r\n" );
document.write( "two of them!\r\n" );
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document.write( "Answer: \r\n" );
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document.write( "so (a,b) = (7,49)\r\n" );
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document.write( "Edwin

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