# Thread: Intervals of a trinomial...

1. ## Intervals of a trinomial...

I've been struggling on this question for the past hour and a half, and I'm really starting to get frustrated.

Find the intervals for which the following inequality holds true. Round to 3 decimal places.

|x^3 - x^2 +x -1| < 3

Obviously, I added one to both sides of the inequality to get
-2 < x^3 - x^2 +x -1 < 4
but I'm completely stumped as to how to simplify the inner trinomial to x. Any help would be greatly appreciated. Thanks!

2. Originally Posted by SpamAndRice
I've been struggling on this question for the past hour and a half, and I'm really starting to get frustrated.

Find the intervals for which the following inequality holds true. Round to 3 decimal places.

|x^3 - x^2 +x -1| < 3

Obviously, I added one to both sides of the inequality to get
-2 < x^3 - x^2 +x -1 < 4
but I'm completely stumped as to how to simplify the inner trinomial to x. Any help would be greatly appreciated. Thanks!
there is a small error you add 1 to both sides but you did not do that for the middle

$\mid x^3-x^2+x-1 \mid <3$

$-3 make into two inequalities then find the intersection for the two solutions

$-3.....(1)

$x^3-x^2+x-1<3$....(2)

(1)
$-3

$0

you need to find the root of the polynomial to study the sign of x^3-x^2+x+2 and take the intervals of x values which make the inequality true but for this there is no exact root there is approximation root you can use intermediate value theorem or you write your question wrong

and for (2) it is same there is no exact root

$x^3-x^2+x-1<3$

$x^3-x^2+x-4<0$