document.write( "Question 905134: Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x = -1, x = 1 + 2i and x = -3i. \n" ); document.write( "

Algebra.Com's Answer #549439 by Fombitz(32388) $\"\"$ $\"About$

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Since the coefficients are real, the complex roots come in complex conjugate pairs.
\n" ); document.write( " $\"P%28x%29=%28x%2B1%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29%28x%2B3i%29%28x-3i%29\"$
\n" ); document.write( " $\"P%28x%29=%28x%2B1%29%28x%5E2-2x%2B5%29+%28x%5E2%2B9%29\"$
\n" ); document.write( " $\"P%28x%29=%28x%5E3-x%5E2%2B3x%2B5%29%28x%5E2%2B9%29\"$
\n" ); document.write( " $\"P%28x%29=x%5E5-x%5E4%2B12x%5E3-4x%5E2%2B27x%2B45\"$ \n" ); document.write( "

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