Question 489050: Okay so I need help finding the real solutions of this equation:
X^4-X^3+2X^2-4X-8=0
I'm pretty sure that I'm supposed to use synthetic division but im not able to figure this out right now. Please help me
Found 2 solutions by dan_math, chessace:
Answer by dan_math(11)   (Show Source):
You can put this solution on YOUR website! yes, you could try the synthetic division for factors of 8
to help you with that, here is the factored form of your equation:
(X-2)(X+1)(X^2+4)=0
Answer by chessace(471)  (Show Source):
You can put this solution on YOUR website! Regroup by even and odd powers:
X^4+2X^2-8 - (X^3+4X)
2nd term = (-) X(X^2+4), so synthetically divide the 1st term by (X^2+4) in hopes of getting a clean factor (you will).
Then express the whole thing as (X^2+4)*(whatever, collect terms).
The 1st of these has no real roots, but the "whatever" will have.
Hint: 2 of them, simple.
Thus the original equation, known to have 4 roots, will have 2 not real, and the 2 you find from "whatever".
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