text: # Thread: polynomial function with 3 zeros
  
  1. ## polynomial function with 3 zeros
  
  i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.
  
  my current work:
  
  f(x)=x(x+3)(x-2i)
  f(x)=(x^2 + 3x)(x-2i)
  f(x)=x^3 - 2ix^2 +3x^2 - 6xi
  
  Just wanting to see if I am doing this problem in the correct way.
  
  i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.
  
  my current work:
  
  f(x)=x(x+3)(x-2i)
  f(x)=(x^2 + 3x)(x-2i)
  f(x)=x^3 - 2ix^2 +3x^2 - 6xi
  
  Just wanting to see if I am doing this problem in the correct way.
  $= x^3 + (3 - 2i) x^2 - 6i x$.
  
  3. Does your problem forbid your function from having additional zeros? If it does no then you could try the function:
  
  f(x)=x(x+3)(x-2i)(x+2i)
  
  So
  
  $f(x)=(x^3 - 2ix^2 +3x^2 - 6xi)(x+2i)$
  $f(x)=(x^4 - 2ix^3 +3x^3 - 6ix^2+2ix^3 + 4x^2 +6ix^2 + 12x)$
  $f(x)=(x^4 +3x^3+ 4x^2 + 12x)$
  
  The advantage of this expression being that the coefficients are all real and it has all of the required zeros.
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