document.write( "Question 1099591: if alpha,beta,gamma,and delta(symbols) are the roots of x^4-2x^3+4x^2+6x-21=0 if alpha + beta =0, solve the equation completely. \n" ); document.write( "

Algebra.Com's Answer #714050 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "if alpha,beta,gamma,and delta(symbols) are the roots of x^4-2x^3+4x^2+6x-21=0 if alpha + beta =0, solve the equation completely.
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document.write( "I will use  \"p\"  and  \"q\"  instead of  and  to make my writing easier.\r\n" );
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document.write( "So, I am given that p and q are the roots of the equation \r\n" );
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document.write( " = 0,\r\n" );
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document.write( "such that  p = -q.  Then the fact that p and q are the roots means\r\n" );
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document.write( " = 0,                (1)     and\r\n" );
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document.write( " = 0,       (2),    or\r\n" );
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document.write( " = 0.                 (3)\r\n" );
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document.write( "Now subtract eq(1) from eq(3) (both sides). You will get\r\n" );
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document.write( " = 0,    or  \r\n" );
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document.write( " = 0.\r\n" );
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document.write( "It implies that  p = +/- .\r\n" );
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document.write( "Thus two roots of the given polynomial are    and  .\r\n" );
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document.write( "Then the polynomial is divisible by   = .\r\n" );
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document.write( "The quotient is  .\r\n" );
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document.write( "The roots of the last quadratic polynomial are    and  .\r\n" );
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document.write( "Thus the roots of the original polynomial are  ,  ,    and  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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