SOLUTION: find a polynomial of degree 4 that has the following zeros -3i, 3i, -2 multiplicity of two

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Question 957948: find a polynomial of degree 4 that has the following zeros -3i, 3i, -2 multiplicity of two

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If z is a zero of a polynomial then (x-z) is a factor of that polynomial. And if the multiplicity of a zero is more than 1, then (x-z) is a factor as many times as the multiplicity.

So if -3i, 3i and -2 with a multiplicty of 2 are zeros then
(x - (-3i)) or (x + 3i) is a factor
(x - 3i) is a factor
(x - (-2)) or (x + 2) is a factor twice.

To find the polynomial, just multiply all the factors:
(x + 3i)*(x - 3i)*(x + 2)*(x + 2)
Hint: The multiplication will be easier if you...
  1. Use the %28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2 pattern to multiply (x + 3i)*(x - 3i). (Remember to replace i%5E2 with -1.)
  2. Use the %28a%2Bb%29%28a%2Bb%29+=+a%5E2%2B2ab%2Bb%5E2 to multiply (x + 2)*(x + 2).
  3. Then multiply the results of the first two multiplcations.