document.write( "Question 1105536: Given that $\"+x%5E2-3x%2B2+\"$ is a factor of $\"+x%5E4%2Bkx%5E3-10x%5E2-20x%2B24+\"$ , evaluate the sum of the four roots of the equation: $\"+x%5E4%2Bkx%5E3-10x%5E2-20x%2B24=0+\"$ \n" ); document.write( "

Algebra.Com's Answer #720391 by ikleyn(52780) $\"\"$ $\"About$

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document.write( " = (x-1)*(x-2),\r\n" );
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document.write( "so 1 and 2 are the roots of the given polynomial of the degree 4.\r\n" );
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document.write( "The fact that x= 1 is the root of the given polynomial of the degree 4 means\r\n" );
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document.write( "1^4 +k*1^3 -10*1^2 - 20*1 + 24 = 0,   or\r\n" );
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document.write( "1 + k - 10 - 20 + 24 = 0,   which implies  k = 5.\r\n" );
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document.write( "According to Vieta's theorem, the sum of the roots of the given polynomial of the degree 4 is equal \r\n" );
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document.write( "to the coefficient at x^3 taken with the opposite sign, i.e. -5.\r\n" );
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