## anonymous 5 years ago X^4-10x^2+24< x^3-4x Write in interval notation, use bracket for single points

1. amistre64

x^2 = -6,4 for the LHS if I did it right in me head. x = 0,2,-2 for the RHS..... I wonder if that helps....

2. amistre64

x^4 +x^3 -10x^2 +4x +24 < 0

3. anonymous

thanks

4. amistre64

that should be ...-x^3.... typo :)

5. anonymous

So, what goes inside the brackets

6. amistre64

dunno yet, still trying to factor it, I got so far: (x-2)(x+2)(x+2)(x-3) We put these on a number line to see which of these makes everything less than 0....

7. amistre64

if I did it right: (-inf,-2) or (2,3)

8. amistre64

the easiest way to determie the values are to draw a number line and put in the values that make the equation equal to zero. Take each value and to the left of it, put a (-) and to the right of it put a (+); then multiply your signs together to get area that are (+) and (-). then pick the areas that fit the equation :)

9. anonymous

I got x3+3x^2-4x-12

10. anonymous

Actually, once you have it factorised, it is probably easier to quickly sketch the graph of the quartic function.

11. amistre64

or do some calculus :)

12. amistre64

X^4-10x^2+24< x^3-4x subtract the RHS from the LHS. x^4 -x^3 -10x^2 +4x +24 >0 right?

13. amistre64

<0 .... typo again... its these fat fingers and this tiny little keyboard :)

14. anonymous

yes

15. amistre64

dont let the "hero" title fool ya, I am after all, just an idiot in disguise :)

16. amistre64

the LHS factors to: (x-2)(x+2)(x-3)(x+2) right? remultiply to check thatits right...

17. anonymous

M Dot cancelled a factor of (x+2) at some point... best not to ever do that with a factor unless you can be sure it is >0 ∀ x ∈ R or it flips the inequality.

18. amistre64

<.......-2.........2.........3.......> - + + + - - + + - - - + -------------------------- - + - + if I did it right, these are my results for the number line....

19. amistre64

but something seems off, the even degree should be positive at both ends...

20. anonymous

The answer is only 2< x <3 , not x<-2

21. amistre64

ahhh..... that seemes more plausible :)

22. anonymous

x^4-10x^2+24\le x^3-4x. The instructor wants x$\epsilon$ and U

23. amistre64

U is the universal set right?

24. anonymous

right

25. amistre64

can you do calculus on it? :)

26. anonymous

This is an algebra class. I'm familiar with any calculus

27. anonymous

I'm not familiar

28. amistre64

bummer.... calculus would allow us to "see" what is happening at cetain points on the graph more easily

29. amistre64

it appears that the graph touches then turns at x = -2 .... which is why it is positive on both sides of it....

30. amistre64

so it "crosses" the x axis at 2 and 3 which make it go negative AND less than 0

31. amistre64

so your notation would be [x|x is an element of (2,3)} or some such notation

32. anonymous

x $\in \cup$

33. amistre64

I am unclear about the "U" set, its been qwhile since I had to play in set theory :)

34. anonymous

Ok, I'm going to go with my gut.

35. amistre64

gut going is good :)

36. anonymous