document.write( "Question 46213: Please help! Find a 5th degree polynomial function with real, rational coefficients and zeros x=0, x=the square root of 3, and x=2-i. I've tried and I just can't figure it out please help. It would be greatly appreciated. \n" ); document.write( "
Algebra.Com's Answer #30696 by venugopalramana(3286)\"\" \"About 
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Please help! Find a 5th degree polynomial function with real, rational coefficients and zeros x=0, x=the square root of 3, and x=2-i.
\n" ); document.write( "MULTIPLY WITH ALL FACTORS OBTAINED FROM THE GIVEN ROOTS
\n" ); document.write( "X=0...X-0=X IS A FACTOR
\n" ); document.write( "X=SQRT(3)....X-SQRT(3) IS A FACTOR..NOW SINCE COEFFICIENTS ARE RATIONAL
\n" ); document.write( "X=-SQRT(3) SHOULD BE A ROOT....X+SQRT(3) IS A FACTOR
\n" ); document.write( "X=2-I........X-2+I IS A FACTOR...SINCE COEFFICIENTS ARE REAL
\n" ); document.write( "X=2+I SHOULD BE A ROOT ...X-2-I IS A FACTOR
\n" ); document.write( "SO MULTIPLYING F(X)=X{X-SQRT(3)}{X+SQRT(3)}{(X-2)+I}{(X-2)-I}=0
\n" ); document.write( "=X(X^2-3)({(X-2)^2-I^2}=0
\n" ); document.write( "X(X^2-3)(X^2-4X+5)=0...MULTIPLY TO GET THE ANSWER\r
\n" ); document.write( "\n" ); document.write( " I've tried and I just can't figure it out please help. It would be greatly appreciated. \n" ); document.write( "
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