SOLUTION: 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 ple

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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.
Found 2 solutions by venugopalramana, Nate:
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
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.
MULTIPLY WITH ALL FACTORS OBTAINED FROM THE GIVEN ROOTS
X=0...X-0=X IS A FACTOR
X=SQRT(3)....X-SQRT(3) IS A FACTOR..NOW SINCE COEFFICIENTS ARE RATIONAL
X=-SQRT(3) SHOULD BE A ROOT....X+SQRT(3) IS A FACTOR
X=2-I........X-2+I IS A FACTOR...SINCE COEFFICIENTS ARE REAL
X=2+I SHOULD BE A ROOT ...X-2-I IS A FACTOR
SO MULTIPLYING F(X)=X{X-SQRT(3)}{X+SQRT(3)}{(X-2)+I}{(X-2)-I}=0
=X(X^2-3)({(X-2)^2-I^2}=0
X(X^2-3)(X^2-4X+5)=0...MULTIPLY TO GET THE ANSWER
I've tried and I just can't figure it out please help. It would be greatly appreciated.

Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!