For anyone who is good at math...

[tjanuranus]

So i'm doing my homework and i came across a problem and i don't understand what it's asking for. The problem is... determine the intervals on which the polynomial is entirely negative and those on which it is entirely positive.

x^2 - 3x - 4

so i factored it out and came with x = 1 and 4. But that's not what the question is asking. What is it asking? lol

[Implode]

Well you did need to factor. Now know the intervals. (-infinite,1),(1,4),(4,infinte). Now there are many ways to find the next part, but you have to find whether the function is positive or negative in those three intervals.

[Jamesman42]

First, x = -1 and 4. And these are important. Double check your factoring.

Draw a number line. Label your x-values (-1, 4). Also, label an arbitrary point between the two numbers, and a point on the opposite sides of both numbers. For example, I labeled -2, 0, and 10. You are going to test all the intervals, from (-inf, -1), (-1,4), and (4, inf).

For x = -2 in the original equation, you get a positive number. Therefore, on (-inf,-1), that interval is positive. The same is true for x = 10, so (4, inf) is an interval on which the polynomial is positive.

For x = 0, it becomes negative. Therefore, the interval (-1, 4) gives you a negative number for that polynomial.

Testing a point on an interval takes care of that whole interval.

Hope that helps!

[Zook]

WHY DO WE NEED TO LEARN THIS?! WE'RE NEVER GOING TO USE IT IN REAL LIFE ANYWAY!

[emindead]

We already have a Maths thread.

[Jamesman42]

WHY DO WE NEED TO LEARN THIS?! WE'RE NEVER GOING TO USE IT IN REAL LIFE ANYWAY!

lol ur rite y go 2 skool rite

[tjanuranus]

thanks guys i'm going to try this out tomorrow.

[Kosmo]

WHY DO WE NEED TO LEARN THIS?! WE'RE NEVER GOING TO USE IT IN REAL LIFE ANYWAY!

I KNOW! THIS IS BULLSHIT! 

[kári]

First, x = -1 and 4. And these are important. Double check your factoring.

Draw a number line. Label your x-values (-1, 4). Also, label an arbitrary point between the two numbers, and a point on the opposite sides of both numbers. For example, I labeled -2, 0, and 10. You are going to test all the intervals, from (-inf, -1), (-1,4), and (4, inf).

For x = -2 in the original equation, you get a positive number. Therefore, on (-inf,-1), that interval is positive. The same is true for x = 10, so (4, inf) is an interval on which the polynomial is positive.

For x = 0, it becomes negative. Therefore, the interval (-1, 4) gives you a negative number for that polynomial.

Testing a point on an interval takes care of that whole interval.

Hope that helps!

Yup. The clue here is that the polynomial only crosses the x-axis in two points, -1 and 4. Those are the only points where the polynomial can change from positive to negative or the other way around. Just pick one point in each of the intervals to find out which one it is.

[Jamesman42]

What's funny is I was at my usual workplace at the college, and there was no one there (in the Math Lab), and I was like "Let me take a break from working on stuff and check the forums." And first thread I see is on math. So I did it all on the whiteboard, just to double-check.

[rumborak]

WHY DO WE NEED TO LEARN THIS?! WE'RE NEVER GOING TO USE IT IN REAL LIFE ANYWAY!

The knowledge of this stuff is almost directly proportional to your later income. Seriously.

rumborak

[Jamesman42]

It's also used extensively in business, economics, and finance, right? I've never taken a business calc class, or had much experience with the financial aspect, but I have seen people bring me problems that involve it.

[Orbert]

WHY DO WE NEED TO LEARN THIS?! WE'RE NEVER GOING TO USE IT IN REAL LIFE ANYWAY!

The knowledge of this stuff is almost directly proportional to your later income. Seriously.

Correct.

y is dollars, x is time, and the polynomial or function is whatever business you're in.  Understand how it all works, or flip burgers for minimum wage the rest of your life.

[reneranucci]

It's also used extensively in business, economics, and finance, right? I've never taken a business calc class, or had much experience with the financial aspect, but I have seen people bring me problems that involve it.

Yep, and I work in those fields. The thing is, when you use it in your job, you forget it's the same tool you learned 10 years before.

[DarkLord_Lalinc]

It's like integration. I mean, it's everywhere.

I think we're so used to computer software making our lives easier that we actually forget how to put our lazy minds to work and make some math.

[tjanuranus]

First, x = -1 and 4. And these are important. Double check your factoring.

Draw a number line. Label your x-values (-1, 4). Also, label an arbitrary point between the two numbers, and a point on the opposite sides of both numbers. For example, I labeled -2, 0, and 10. You are going to test all the intervals, from (-inf, -1), (-1,4), and (4, inf).

For x = -2 in the original equation, you get a positive number. Therefore, on (-inf,-1), that interval is positive. The same is true for x = 10, so (4, inf) is an interval on which the polynomial is positive.

For x = 0, it becomes negative. Therefore, the interval (-1, 4) gives you a negative number for that polynomial.

Testing a point on an interval takes care of that whole interval.

Hope that helps!

Yes i do understand it now. The problem is my teacher goes really fast and doesn't explain things in detail. So i go to the book it really blows! I don't like this book at all. And it's been a long time since i've done this stuff.

[Jamesman42]

Teachers have the task of having to cover so many things, so sometimes they have to race through. It sucks, but they are caught in that dilemma. A really great teacher could probably fit it all in the school year with good understanding.

[tjanuranus]

ok last question on this topic. Some kind of problem but i'm not getting the correct answer. This one i have the answer for. The problem is...

2x^2-4x-3

so i use the quadratic formula and i came up with

4+- sqrt of -4^2 - 4(2)(-3) all divided by 2(2)

4+- sgrt of 40 all divided by 4

4+- 3sgrt of 5 all divided by 4

1 +- 3sqrt of 5....

But that part is wrong what the hell? the book says. 2 +- sqrt of 10 all divided by 2.

[Jamesman42]

a = 2, b = -4, c = -3

x = [4 +/- sqrt(16 +24)]/4 ...(Quadratic Formula, I didn't show every little simplification)

= [4 +/- 2*sqrt(10)]/4 ...(Simplify radical, sqrt(40) = sqrt(4*10) = 2*sqrt(10))

= [2 +/- sqrt(10)]/2 ...(Cancel by a factor of 2 on ALL terms)

That's the answer your book has.

[Orbert]

How did you get from sqrt(40) to 3sqrt(5)?
sqrt(40) reduces to 2sqrt(10)
Then divide everything by 2 to get the book's answer.

[Orbert]

Whoa, James is faster on the draw again!

[tjanuranus]

ok so i guess my question is why are you using 4 as the perfect square when nine is a greater perfect square? I must have forgotten the rule. This is my first semester in college and i graduated high school in 99! So yeah it's taking me a bit of time to get it all back.

[tjanuranus]

How did you get from sqrt(40) to 3sqrt(5)?
sqrt(40) reduces to 2sqrt(10)
Then divide everything by 2 to get the book's answer.

because 9 times 5 is 40. so 3sqrt of 5. well that's what i was thinking!

[Jamesman42]

Because 4 is the biggest square number that goes into 40. Like, 9 does not divide 40. That's why you wouldn't use 9.

[Jamesman42]

How did you get from sqrt(40) to 3sqrt(5)?
sqrt(40) reduces to 2sqrt(10)
Then divide everything by 2 to get the book's answer.

because 9 times 5 is 40. so 3sqrt of 5. well that's what i was thinking!

8*5 = 40, 9*5 = 45.

[tjanuranus]

How did you get from sqrt(40) to 3sqrt(5)?
sqrt(40) reduces to 2sqrt(10)
Then divide everything by 2 to get the book's answer.

because 9 times 5 is 40. so 3sqrt of 5. well that's what i was thinking!

8*5 = 40, 9*5 = 45.

OHHHHHHHHHH MYYYYYYYYYYYY GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOD

[Jamesman42]

Whoa, James is faster on the draw again!

I've been doing this a lot lately, and I'll be starting Tutor.com, which will be online calculus tutoring. Gotta be fast.

[jsem]

James is legendary lol

[tjanuranus]

Whoa, James is faster on the draw again!

I've been doing this a lot lately, and I'll be starting Tutor.com, which will be online calculus tutoring. Gotta be fast.

wow that's awesome. I'm in pre calculous now but in order to get my CS transfer degree i need calc 1, calc, 2 and linear algebra. i might need to sign up!

[Jamesman42]

Whoa, James is faster on the draw again!

I've been doing this a lot lately, and I'll be starting Tutor.com, which will be online calculus tutoring. Gotta be fast.

wow that's awesome. I'm in pre calculous now but in order to get my CS transfer degree i need calc 1, calc, 2 and linear algebra. i might need to sign up!

Nah man, they'll make you pay for it. Why not ask me here for free?

Or I'll take paypal for $2 a problem.

[Vivace]

First, x = -1 and 4. And these are important. Double check your factoring.

Draw a number line. Label your x-values (-1, 4). Also, label an arbitrary point between the two numbers, and a point on the opposite sides of both numbers. For example, I labeled -2, 0, and 10. You are going to test all the intervals, from (-inf, -1), (-1,4), and (4, inf).

For x = -2 in the original equation, you get a positive number. Therefore, on (-inf,-1), that interval is positive. The same is true for x = 10, so (4, inf) is an interval on which the polynomial is positive.

For x = 0, it becomes negative. Therefore, the interval (-1, 4) gives you a negative number for that polynomial.

Testing a point on an interval takes care of that whole interval.

Hope that helps!

Yes i do understand it now. The problem is my teacher goes really fast and doesn't explain things in detail. So i go to the book it really blows! I don't like this book at all. And it's been a long time since i've done this stuff.

Talk to the teacher during office hours if you don't understand something. I did this during Diffy Qs and believe me if I never spoke to the teacher about my questions I would have flunked that class. Instead I got 92% on the class. Tip. If you plan on taking further math down the road, KNOW THIS STUFF!!! This is foundational knowledge for higher level math. It only gets harder from here. I'm assuming this is Algebra 2? It's been a while.

[tjanuranus]

This is pre calculous

[Orbert]

In my experience, "Pre-Calculus" was kinda interchangeable with "Algebra II/Trigonometry" so Vivace is also correct.  This was also my favorite stuff to learn, and to teach.  It's where all that arithmetic, algebra, geometry, and trigonometry you've been building for years finally start coming together in a meaningful way, giving you a glimpse of "the big picture."

[tjanuranus]

ok having a weird issue here. Since you said you don't me asking.. lol

solve by factoring..

(x+a)^2-b^2=0

Here is what i did. extracting square roots and got..

x+a-b= +- Sqrt. of 0

then x=-a+b
which the book says is right.
then x=a-b
which the book says is wrong. supposed to be -a-b. HOW?

[Fiery Winds]

You can't take the square root of two terms added or subtracted together.  Move the -b^2 term to the other side first and you'll get your answer.  You got lucky with your first answer.