Yes, I just figured out how to work it.Hello, and welcome to FMH!
Do you mean:
[MATH]f(x)=ax^3-15x^2+bx+15[/MATH] ?
Yes, x is one of the values. And X is because it is an inequality. So it is apart of the "therefore" statement (x is an element of...)If you would like to be helped then please write a clear post.
Did you mean to have x and X? What does XE(3,5) mean??
In defining f(x) you had 15x^2X. Did you mean that?
Also, please read the guidelines so that you can receive help.
yes, I figured that because it was an inequality that XE(3,5) were x-ints and used the remainder theorem from there. but I'm just stuck at the stage before identifying the variables...unless that's wrong....I would begin by observing that:
[MATH]f(3)=0[/MATH]
[MATH]f(5)=0[/MATH]
This will give us two equations in two unknowns. Can you proceed?
yes, I figured that because it was an inequality that XE(3,5) were x-ints and used the remainder theorem from there. but I'm just stuck at the stage before identifying the variables...unless that's wrong....
Thank you!Presumably the problem is:
Given [MATH]f(x)=ax^3-15x^2+bx+15[/MATH], when [MATH]x\in (3,5), f(x)\lt0[/MATH].
I think we have to assume it means that (3, 5) is one of the entire intervals on which f(x) is negative (not just a subset of such an interval!), so that f(x) = 0 at 3 and 5. That allows you to find a and b, and then you can find the other zero of f.
I don't know what those are, sorry. Can you clarify?I'm getting integral values.
I don't know what those are, sorry. Can you clarify?
I'm getting values that are integers. Can you write a simplified form of the system of equations and we can go from there?
ahahaha i'm having a blonde moment right now...
I got 27a + 3b -120 = 0
and 125a + 5b -360 = 0
does that seem right on your end?
Okay, I got a = 2 and b = 22. yes?Yes, those look good...I would even consider dividing the first equation by 3 and the second by -5 to get
[MATH]9a+b-40=0[/MATH]
[MATH]-25a-b+72=0[/MATH]
Now add the equations...what do you get?
Okay, I got a = 2 and b = 22. yes?
so you get f(x) = 23-152+22+15Yes, that's what I get too. Can you now find the third zero of the cubic function?
whoops, forgot the x's on that last equationYes, that's what I get too. Can you now find the third zero of the cubic function?