Question 1086482: Find a polynomial that has the following characteristics. Show your work.
-Its degree is seven.
-It has only integer coefficients.
-Its zero include -1 as only rational ones.
-Its zero include 4i (multiplicity 1) and -2root(2)(multiplicity 1).
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! -Its degree is seven.
-It has only integer coefficients.
 , , , , , , are integers
-Its zero include  as only rational ones.
-Its zero include  (multiplicity 1) and -2root(2)(multiplicity 1).
since complex roots and square root always come in pairs, we will have  and  too
since we need seven roots, we use three times
and, using zero product theorem we have:
when all multiplied, we get
 which is your polynomial
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