Find the smallest integer problem

[Sportslover]

Hi, I am stuck trying to do the following two problems. I would appreciate any help you can provide and if you could please break the steps down. I've searched all over google for a way to do these and cannot find anything remotely close to finding an answer. I don't even know what you would call a problem like this. Thank you in advance:

1. Find the smallest integer X that makes Y positive when Y=0.000000001(x^3) - 100000(x^2)

2. Find the smallest integer X that makes Y negative when Y=-0.000000001(x^3) - 10000000(x^2)

 

[Deleted member 4993]

Hi, I am stuck trying to do the following two problems. I would appreciate any help you can provide and if you could please break the steps down. I've searched all over google for a way to do these and cannot find anything remotely close to finding an answer. I don't even know what you would call a problem like this. Thank you in advance:

1. Find the smallest integer X that makes Y positive when Y=0.000000001(x^3) - 100000(x^2)

2. Find the smallest integer X that makes Y negative when Y=-0.000000001(x^3) - 10000000(x^2)

Hint: Factorize and remember x^2 is always positive.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[Sportslover]

Still Confused

Hello,

I am a an adult student trying to complete an algebra screening for a class to evaluate where I am at. That is why I need some help.

I know what factoring is but I don't know what I'm factoring. Cancel all the zeros I can??? I've never seen a problem like this before so I don't know where to begin. What do you call what I am supposed to be doing here? I also don't understand why x^2 is positive when there's a negative sign in front of it.

Thank you.

 

[Deleted member 4993]

Hello,

I am a an adult student trying to complete an algebra screening for a class to evaluate where I am at. That is why I need some help.

I know what factoring is but I don't know what I'm factoring. Cancel all the zeros I can??? I've never seen a problem like this before so I don't know where to begin. What do you call what I am supposed to be doing here? I also don't understand why x^2 is positive when there's a negative sign in front of it.

Thank you.

I personally don't think you should seek help - while preparing for a screening test. That defeats the purpose of the screening test. If you "hood-wink" the screening test and get in - you would be swimming upstream. And that won't be pleasant. Actually it will be miserable. If you need to - take a regular algebra classes and learn these things so that you can use those.

 

[ksdhart]

I concur with Subhotosh Khan's assessment. There's no shame in admitting your math skills are rusty after years of non-use (or maybe that they were never that good in the first place). As for your question about x^2 being positive even though there's a negative sign, let's consider what the expression really says. The relevant part is:

-100000(x^2) = -100000 * (x^2)

Here, the negative sign is attached only to the 100000 term. Now consider if we had this instead:

-100000(5) = -100000 * 5

Again, the negative sign is attached only to the 100000 term. Overall, the whole expression is indeed negative. That's because we have a negative term (-100000) times a positive term (5). But the 5 term is always positive, no matter whether the expression has a negative sign or not. Can you see why similar logic applies to the x^2 term?

 

[Sportslover]

I personally don't think you should seek help - while preparing for a screening test. That defeats the purpose of the screening test. If you "hood-wink" the screening test and get in - you would be swimming upstream. And that won't be pleasant. Actually it will be miserable. If you need to - take a regular algebra classes and learn these things so that you can use those.

I'm not trying to hood wink any test. I'm actually trying to learn how to do these problems. This is not the only thing on the screening test and I've grasped every other concept I think will appear. I'd like to learn how to do these as well. I just have never seen this format of a problem in high school and not sure what's being asked.

 

[ksdhart]

Well, let's take a look at what's going on. We have two variables x and y, which is a function of x. We're told to find the smallest integer value of x, such that y is positive. That places constraints on our variables and allows us to find a solution. What would you have done if you'd been given this similar, but much easier, problem?

Find the smallest integer x, such that y is positive, given y = 2x² - 4x

As a further hint, you might make the problem easier by writing it in a different form. For instance, can you write 0.000000001 as a power of 10? And can you do the same for 100000? Then what do you notice?

 

[Steven G]

Hi, I am stuck trying to do the following two problems. I would appreciate any help you can provide and if you could please break the steps down. I've searched all over google for a way to do these and cannot find anything remotely close to finding an answer. I don't even know what you would call a problem like this. Thank you in advance:

1. Find the smallest integer X that makes Y positive when Y=0.000000001(x^3) - 100000(x^2)

2. Find the smallest integer X that makes Y negative when Y=-0.000000001(x^3) - 10000000(x^2)

I concur with Subhotosh as well.
I will explain why x^2 is always positive (or 0) even if there is a negative sign in front of it,
3 is positive. -3 is negative, But the 3 that come to the right of the negative sign is 3 and is positive. Just because you put a negative sign in front of 3 it does NOT make 3 a negative number. Yes, -3 is a negative number but 3 is not. Maybe, for you, it would have been better to say that -x^2 is always negative (or 0). Again the reason is that x^2 is always positive (or 0) and when you put a negative sign in front of it then it becomes negative (or 0). I hope this has helped.