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.
------
f(x) = (x-3i)(x+3i)(x+2)(x-4)
-----
= (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
|
|
|
