Question

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

Answer 1

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....

Answer 2

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

Answer 3

thanks

Answer 4

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

Answer 5

So, what goes inside the brackets

Answer 6

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....

Answer 7

if I did it right:

(-inf,-2) or (2,3)

Answer 8

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 :)

Answer 9

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

Answer 10

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

Answer 11

or do some calculus :)

Answer 12

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

x^4 -x^3 -10x^2 +4x +24 >0 right?

Answer 13

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

Answer 14

yes

Answer 15

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

Answer 16

the LHS factors to:

(x-2)(x+2)(x-3)(x+2) right? remultiply to check thatits right...

Answer 17

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.

Answer 18

<.......-2.........2.........3.......>
- + + +
- - + +
- - - +
--------------------------
- + - +

if I did it right, these are my results for the number line....

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

x^4-10x^2+24\le x^3-4x.

The instructor wants x\[\epsilon\] and U

Answer 23

U is the universal set right?

Answer 24

right

Answer 25

can you do calculus on it? :)

Answer 26

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

Answer 27

I'm not familiar

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

x \[\in \cup\]

Answer 33

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

Answer 34

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

Answer 35

gut going is good :)

Answer 36

thank you for your help