SOLUTION: Find a polynomial function with integer coefficients and of least possible degree with zeros 1, 2, -3, -3i

Question 1013336: Find a polynomial function with integer coefficients and of least possible
degree with zeros 1, 2, -3, -3i
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Since -3i is a zero, in order to have integer coefficients,
it must also have its conjugate +3i as a zero also:

  x=1,   x=2,   x=-3,   x=-3i,  x=3i

x-1=0, x-2=0, x+3=0, x+3i=0, x-3i=0

  (x-1)(x-2)(x+3)(x+3i)(x-3i) = 0

Multiply that out, collect like terms, (big job),
and get:



That's the function set = 0 to find the zeros,
so the function is



Edwin

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