help ASAP!

[HelpMehhhhh]

Write a polynomial inequality with a quartic function that is > 0 (greater than zero) on the interval
(−5, −5/2) ∪ (1 − √2, 1 + √2). Express the factors with rational coefficients. You do not need to expand.

Above question is confusing and can't seem to understand it

 

[tkhunny]

If it ">0" on (-5,-5/2), what does that say about where it might be "<0" or where it crosses the x-axis?

 

[HelpMehhhhh]

If it ">0" on (-5,-5/2), what does that say about where it might be "<0" or where it crosses the x-axis?

sorry I couldn't understand, could you clarify?

 

[tkhunny]

Here is a function that is positive on (0,1)

What is it AT x = 0 and AT x = 1?

What is it immediately left of x = 0?
What is it immediately right of x = 1?

 

[HelpMehhhhh]

If it ">0" on (-5,-5/2), what does that say about where it might be "<0" or where it crosses the x-axis?

I'm understandng it now but I don't understand how to format it? would it be a function, if so I don't understand how to create one with so little information or am I supposed to do something else?

 

[tkhunny]

The limits of the ranges are the zeros. Your only problem is the irrational ones. The problem says rational coefficients.

 

[HelpMehhhhh]

The limits of the ranges are the zeros. Your only problem is the irrational ones. The problem says rational coefficients.

could you give an example, I don't know why im having such a hard time understanding this

 

[tkhunny]

This is all you need:

If a polynomial function crosses the x axis at x = a, then (x-a) is a factor of the polynomial.
Further, if it is a single factor (x-a) and NOT (x-a)^2, then the function will be positive on one side and negative on the other side.

This should be in your course materials.

 

[HelpMehhhhh]

This is all you need:

If a polynomial function crosses the x axis at x = a, then (x-a) is a factor of the polynomial.
Further, if it is a single factor (x-a) and NOT (x-a)^2, then the function will be positive on one side and negative on the other side.

This should be in your course materials.

so how do I respond to the question then? the issue im having is that I can't seem to draw it as a quartic function, im given intervals that are in Quadrant III and II and no specific roots to go off of

 

[tkhunny]

That is incorrect. You are specifically given all four roots. They are the ends of the intervals.

 

[Dr.Peterson]

Write a polynomial inequality with a quartic function that is > 0 (greater than zero) on the interval
(−5, −5/2) ∪ (1 − √2, 1 + √2). Express the factors with rational coefficients. You do not need to expand.

Above question is confusing and can't seem to understand it

so how do I respond to the question then? the issue im having is that I can't seem to draw it as a quartic function, im given intervals that are in Quadrant III and II and no specific roots to go off of

Please explain the comment about quadrants. The intervals are on the x-axis, which is not in any quadrants.

Are you possibly confusing intervals with ordered pairs, and thinking it's somehow talking about the points (−5, −5/2) and (1 − √2, 1 + √2), which are in quadrants III and II? It is not!

It's saying that f(x) > 0 when −5 < x < −5/2 or 1 − √2 < x < 1 + √2. Assuming it means that this is the entire set on which the function is positive, that implies that f(x) = 0 for x = −5, −5/2, 1 − √2, or 1 + √2. Those are your four zeros ("roots").

 

[HelpMehhhhh]

That is incorrect. You are specifically given all four roots. They are the ends of the intervals.

I feel so stupid honestly, I fogot how intervals worked! I see why I couldn't understand it now. Thanks!

 

[HelpMehhhhh]

Please explain the comment about quadrants. The intervals are on the x-axis, which is not in any quadrants.

Are you possibly confusing intervals with ordered pairs, and thinking it's somehow talking about the points (−5, −5/2) and (1 − √2, 1 + √2), which are in quadrants III and II? It is not!

It's saying that f(x) > 0 when −5 < x < −5/2 or 1 − √2 < x < 1 + √2. Assuming it means that this is the entire set on which the function is positive, that implies that f(x) = 0 for x = −5, −5/2, 1 − √2, or 1 + √2. Those are your four zeros ("roots").

exactly, I confused them, the how part is beyond me though!

 

[Dr.Peterson]

I suspect you are panicked and your mind has shut down, or at least got stuck in wrong interpretations. I recommend stepping away from the computer, taking a walk, and then coming back to these problems fresh. Then you should be able to take what you've been told and solve the problem. Trust yourself to be able to solve it; don't waste time begging someone else to do what your mind can do if you take a deep breath and try.