help with inequality

[milanna]

Hi,

I am having trouble with the inequality:

x^2 - 3x + 2 >= 0

thank you

 

[stapel]

First step: factor. Then find the zeroes. The zeroes (there will be two of them) will split the number line (negative infinity to positive infinity) into three intervals.

You need to find the interval(s) on which x² - 3x + 2 is positive. So either pick one value inside each interval, plugging the values into "x² - 3x + 2" and checking the sign (plus or minus) on the answer, or else just think about the graph of a positive quadratic. Where is that sort of quadratic above the x-axis (positive) and below the x-axis (negative)? You want the interval(s) where the graph is above the x-axis.

Oh, and since this is an "or equal to" inequality, you'll need to include the zeroes in the solution as well.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[milanna]

x^2 - 3x + 2 >= 0

I factored and got

(x-2)(x-1) >= 0
x=2 x=1

But I don't know where to go from here.

 

[pka]

Your roots divide the real line into three regions: \(\displaystyle ( - \infty ,1] \cup [1,2] \cup [2,\infty )\).

Now you try numbers in each set to see which work.

 

[milanna]

Ok, I got a final answer of (I think)

(- infinity, 1] U [2, infinity)


How did you make the little infinity symbol? :?

Thanks for the help everyone.

 

[pka]

Look at the very top of this page.
There is a tab labeled “FORUM HELP”, pull it down.
There you will find symbol help.
Using TeX is best. If you use Windows try TeXaide.

 

[Matt]

Ok, I got a final answer of (I think)

(- infinity, 1] U [2, infinity)


How did you make the little infinity symbol? :?

More specifically, you would type:

[tex]\(-\infty,1]\cup[2,\infty)[/tex]

and the result is:

\(\displaystyle \qquad\(-\infty,1]\cup[2,\infty)\)

Like pka said, you can find LaTeX references which can help you to learn LaTeX. But be warned, the LaTeX here is incomplete; a lot of commands are missing.

In the future, if you'd like to see how someone wrote his code, then you can click on the "quote" button (which appears in the upper-right hand corner of every post) in order to see the contents of the post.