SOLUTION: please help its for a project at school, i need to find the solution set including complex solutions, if any, of this rational equation {{{ (x^5-62x^3-175439x)/(x^2-451)=0 }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help its for a project at school, i need to find the solution set including complex solutions, if any, of this rational equation {{{ (x^5-62x^3-175439x)/(x^2-451)=0 }}}      Log On


   

Question 439568: please help its for a project at school, i need to find the solution set including complex solutions, if any, of this rational equation
+%28x%5E5-62x%5E3-175439x%29%2F%28x%5E2-451%29=0+
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x%5E5-62x%5E3-175439x%29%2F%28x%5E2-451%29=0+
Every term in the numerator has an x in it,
so factor out an x
+%28x%2A%28x%5E4-62x%5E2-175439%29%29%2F%28x%5E2-451%29=0+
On my calculator I did +175439%2F451+=+389+
so, I guessed that the numerator could be factored as:
+%28x%2A%28x%5E2+-+451%29%2A%28x%5E2+%2B+389%29%29%2F%28x%5E2-451%29=0+
This worked out exactly right, so cancelling, I get:
+%28x%2A%28x%5E2+%2B+389%29%29=0+
The solutions are:
x+=+0
and
+x%5E2+%2B+389+=+0+
+x%5E2+=+-389+
+x+=+sqrt%28-389%29
+x+=+19.723i+
and
+x+=+-19.723i+ (the negative square root)
You can check by plugging this back into original equation

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Check to see if 451 is a factor of 175439.
If it is, see if you can factor the numerator.