document.write( "Question 1089213: x^4 - x^3 + x^2 - x + 1 = 0 \n" ); document.write( "

Algebra.Com's Answer #703568 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "If you multiply both sides of your equation by (x+1), you will get the equation\r\n" );
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document.write( "x^5 + 1 = 0,   or   x^5 = -1.\r\n" );
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document.write( "Its roots are the roots of degree 5 of -1   (one real root -1 and the others are complex roots).\r\n" );
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document.write( "Therefore, the roots of the original equation are all four complex roots of the degree 5  of -1.\r\n" );
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document.write( "They are \r\n" );
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document.write( "1)  cos(36°) + i*sin(36°);\r\n" );
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document.write( "2)  cos(108°) + i*sin(108°);\r\n" );
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document.write( "3)  cos(252°) + i*sin(252°);\r\n" );
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document.write( "4)  cos(324°) + i*sin(324°).\r\n" );
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