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 #720382 by Boreal(15235) $\"\"$ $\"About$

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x^2-3x+2 factors into (x-2)(x-1), so x=1 and 2 are roots.
\n" ); document.write( "x^4+kx^3-10x^2-20x+24=0
\n" ); document.write( "16+8k-40-40+24=0
\n" ); document.write( "8k-40=0
\n" ); document.write( "k=5
\n" ); document.write( "the polynomial is x^4+5x^3-10x^2-20x+24
\n" ); document.write( "synthetic division with 2\r
\n" ); document.write( "\n" ); document.write( "2/1===5===-10===-20===24
\n" ); document.write( "==1==7=====4=====-12===0
\n" ); document.write( "x^3+7x^2+4x-12
\n" ); document.write( "-2/1===7===4===-12
\n" ); document.write( "==1===5===-6===0
\n" ); document.write( "x^2+5x-6, so -2 is a root
\n" ); document.write( "(x+6)(x-1)=0, and 1 is already known to be a root, so -6 is the other root.
\n" ); document.write( "The sum of -6, -2, 1, 2 is -5. ANSWER.
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-1000%2C1000%2Cx%5E4%2B5x%5E3-10x%5E2-20x%2B24%29\"$ \n" ); document.write( "

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