SOLUTION: PLEASE HELP Write the equation of the function whose roots are -3i, -2, and 4

Algebra.Com
Question 706040: PLEASE HELP
Write the equation of the function whose roots are
-3i, -2, and 4
Found 2 solutions by stanbon, Edwin Parker:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Write the equation of the function whose roots are
-3i, -2, and 4
----
If you want to avoid having complex number coefficients,
+3i must also be a root.
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f(x) = (x-3i)(x+3i)(x+2)(x-4)
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= (x^2+9)(x^2-4x-8)
----
= x^4-4x^3-8x^2+9x^2-36x-72
----
= x^4-4x^3+x^2-36x-72
==========================
Cheers,
Stan H.
================
Answer by Edwin Parker(36)   (Show Source): You can put this solution on YOUR website!

The other tutor made an error.

Since -3i is a root so is its conjugate 3i.  
That's because -3i is 0-3i and its conjugate is 0+3i or just 3i.

So the roots are

 x=-3i,   x=3i,  x=-2,   x=4

x+3i=0, x-3i=0, x+2=0, x-4=0

(x+3i)·(x-3i)·(x+2)·(x-4) = 0

        (x²-9i²)(x²-2x-8) = 0
      [x²-9(-1)](x²-2x-8) = 0
          (x²+9)(x²-2x-8) = 0

Multiply that out and collect terms and get:

         x4-2x³+x²-18x-72 = 0

Edwin
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