document.write( "Question 1100423: Form the fifth-degree polynomial function with real coefficients,
\n" ); document.write( "given that 1+i is a zero, and that the graph passes through (-2,0),
\n" ); document.write( "(0,8)(1,0) \n" ); document.write( "

Algebra.Com's Answer #714916 by Fombitz(32388) $\"\"$ $\"About$

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Polynomials with complex roots and real coefficients must have complex roots as complex conjugate pairs.
\n" ); document.write( "So if $\"11%2Bi\"$ is a root, so is $\"11-i\"$ .
\n" ); document.write( " $\"f%28x%29=+%28x-%2811%2Bi%29%29%28x-%2811-i%29%29%28x%2B2%29%28x-1%29+%28x-a%29\"$
\n" ); document.write( "You don't know what $\"a\"$ is but we will get it using the point (0,8).
\n" ); document.write( " $\"f%28x%29=%28x%5E2-22x%2B122%29%28x%5E2%2Bx-2%29%28x-a%29\"$
\n" ); document.write( " $\"f%28x%29=%28x%5E4-21x%5E3%2B98x%5E2%2B166x-244%29%28x-a%29\"$
\n" ); document.write( "So when $\"x=0\"$ ,
\n" ); document.write( " $\"8=%280-0%2B0%2B0-244%29%28-a%29\"$
\n" ); document.write( " $\"a=8%2F244\"$
\n" ); document.write( " $\"a=2%2F61\"$
\n" ); document.write( " $\"f%28x%29=%28x%5E4-21x%5E3%2B98x%5E2%2B166x-244%29%28x-2%2F61%29\"$
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