SOLUTION: Find all the roots. x^4 + 11x^2 + 18 = 0

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Question 1020787: Find all the roots.
x^4 + 11x^2 + 18 = 0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Make the substitution:
+z+=+x%5E2+
+x%5E4+%2B+11x%5E2+%2B+18+=+0+
+z%5E2+%2B+11z+%2B+18+=+0+
By looking at this:
+%28+z+%2B+9+%29%2A%28+z+%2B+2+%29+=+0+
+z+=+-9+
+z+=+-2+
--------------
Plug these results back into substitution
+z+=+x%5E2+
+-2+=+x%5E2+
+x+=+sqrt%282%29%2Ai+
and, also:
+x+=+-sqrt%282%29%2Ai+
-----------------
+-9+=+x%5E2+
+x+=+3i+
+x+=+-3i+
--------------
The roots are:
+sqrt%282%29%2Ai+ , +-sqrt%282%29%2Ai+ , +3i+ , +-3i+
-----------------------
check answer:

+%28+x%5E2+%2B+2+%29%2A%28+x%5E2+%2B+9+%29+
+x%5E4+%2B+11x%5E2+%2B+18+=+0+
OK