document.write( "Question 631393: if a+b+c=0 and a,b,c are rational then the roots of the equation (b+c-a)x²+(c+a-b)x+(a+b-c)=0 are \n" ); document.write( "

Algebra.Com's Answer #397535 by AnlytcPhil(1810) $\"\"$ $\"About$

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if a+b+c=0 and a,b,c are rational then the roots of the equation \r
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document.write( "That's\r\n" );
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document.write( "[(b+c)-a]x² + [(c+a)-b]x + [(a+b)-c] = 0\r\n" );
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document.write( "Solve a+b+c = 0 for (b+c), (c+a), and (a+b)\r\n" );
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document.write( "        b+c = -a\r\n" );
document.write( "        c+a = -b\r\n" );
document.write( "        a+b = -c\r\n" );
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document.write( "Substituting these into\r\n" );
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document.write( "[(b+c)-a]x² + [(c+a)-b]x + [(a+b)-c] = 0\r\n" );
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document.write( "         [-a-a]x² + [-b-b]x + [-c-c] = 0\r\n" );
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document.write( "                     -2ax² - 2bx -2c = 0\r\n" );
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document.write( "                        ax² + bx + c = 0\r\n" );
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document.write( "That's just the general quadratic equation.  So its roots are given\r\n" );
document.write( "by the quadratic formula:\r\n" );
document.write( "                           \r\n" );
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document.write( "Edwin

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