1. solve for x, xER using algebraic methods. Use a table to show your results.

$\displaystyle x^3-2x^2-x+2 > 0$

Can someone please guide me on this one?

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- Mar 9th 2009, 12:47 PMwilliamsolving inequality
1. solve for x, xER using algebraic methods. Use a table to show your results.

$\displaystyle x^3-2x^2-x+2 > 0$

Can someone please guide me on this one? - Mar 9th 2009, 01:00 PMMoo
Hello,

Factor $\displaystyle x^3-2x^2-x+2$

you can see that 1 is a root of this polynomial. Thus (x-1) is a factor of the polynomial.

solve for a,b in $\displaystyle x^3-2x^2-x+2=(x-1)(x^2+ax+b)$

you'll get two roots, p and q :

$\displaystyle x^3-2x^2-x+2=(x-1)(x-p)(x-q)$

(p=-1 and q=2)

then make a table, like they said :

between - infinity and -1, (x-1)<0, (x+1)<0, (x-2)<0, so the polynomial is...

between -1 and 1, ...

between 1 and 2, ...

between 2 and infinity, ...

if you have no idea on how to do this, just say it here, but please try to think about it :)