document.write( "Question 889313: Thank you for your help solving. \r
\n" ); document.write( "\n" ); document.write( "Solve x^4 - 2x^3 + 7x^2 - 10x + 10 = 0 given that 1 + i is a root. \n" ); document.write( "

Algebra.Com's Answer #538072 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
If $\"1%2Bi\"$ is a root, then $\"1-i\"$ is also a root since complex roots only occur in complex conjugate pairs.
\n" ); document.write( " $\"%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-%281-i%29x-%281%2Bix%29-%281%2Bi%29%281-i%29\"$
\n" ); document.write( " $\"%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-2x%2B%281-i%2Bi-i%5E2%29%29\"$
\n" ); document.write( " $\"%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-2x%2B%281%2B1%29%29\"$
\n" ); document.write( " $\"%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-2x%2B2%29\"$
\n" ); document.write( "Now use polynomial long division to factor out this polynomial.
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.
\n" ); document.write( "Symbolically shown here, the divisor turns out to be,
\n" ); document.write( " $\"x%5E2%2B5\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"x%5E4+-+2x%5E3+%2B+7x%5E2+-+10x+%2B+10=%28x%5E2-2x%2B2%29%28x%5E2%2B5%29\"$
\n" ); document.write( "So the other two roots are also complex,
\n" ); document.write( " $\"x=0+%2B-+5i\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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