SOLUTION: Find a polynomial fucntion of 5th degree given the following zeros. -4, -2i, √6

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Question 61312: Find a polynomial fucntion of 5th degree given the following zeros.
-4, -2i, √6
Answer by venugopalramana(3286) About Me  (Show Source):
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Find a polynomial fucntion of 5th degree given the following zeros.
-4, -2i, √6
ASSUMING THE POLYNOMIAL TO BE WITH REAL COEFFICIENTS,THE CONJUGATES OF COMPLEX AND IRRATIONAL NUMBERS WILL ALSO BE THE ROOTS. HENCE THE 5 ROOTS ARE
-4,-2I,+2I,SQRT(6),-SQRT(6)...HENCE THE POLYNOMIAL IS
P = (X+4)(X+2I)(X-2I)[X+SQRT(6)][X-SQRT(6)]=0
P=(X+4)(X^2+4)(X^2-6)=0
P=(X+4)(X^4-2X^2-24)=0
P=X^5+4X^4-2X^3-8X^2-24X-96=0