anonymous
  • anonymous
X^4-10x^2+24< x^3-4x Write in interval notation, use bracket for single points
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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amistre64
  • 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....
amistre64
  • amistre64
x^4 +x^3 -10x^2 +4x +24 < 0
anonymous
  • anonymous
thanks

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amistre64
  • amistre64
that should be ...-x^3.... typo :)
anonymous
  • anonymous
So, what goes inside the brackets
amistre64
  • 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....
amistre64
  • amistre64
if I did it right: (-inf,-2) or (2,3)
amistre64
  • 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 :)
anonymous
  • anonymous
I got x3+3x^2-4x-12
anonymous
  • anonymous
Actually, once you have it factorised, it is probably easier to quickly sketch the graph of the quartic function.
amistre64
  • amistre64
or do some calculus :)
amistre64
  • 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?
amistre64
  • amistre64
<0 .... typo again... its these fat fingers and this tiny little keyboard :)
anonymous
  • anonymous
yes
amistre64
  • amistre64
dont let the "hero" title fool ya, I am after all, just an idiot in disguise :)
amistre64
  • amistre64
the LHS factors to: (x-2)(x+2)(x-3)(x+2) right? remultiply to check thatits right...
anonymous
  • 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.
amistre64
  • amistre64
<.......-2.........2.........3.......> - + + + - - + + - - - + -------------------------- - + - + if I did it right, these are my results for the number line....
amistre64
  • amistre64
but something seems off, the even degree should be positive at both ends...
anonymous
  • anonymous
The answer is only 2< x <3 , not x<-2
amistre64
  • amistre64
ahhh..... that seemes more plausible :)
anonymous
  • anonymous
x^4-10x^2+24\le x^3-4x. The instructor wants x\[\epsilon\] and U
amistre64
  • amistre64
U is the universal set right?
anonymous
  • anonymous
right
amistre64
  • amistre64
can you do calculus on it? :)
anonymous
  • anonymous
This is an algebra class. I'm familiar with any calculus
anonymous
  • anonymous
I'm not familiar
amistre64
  • amistre64
bummer.... calculus would allow us to "see" what is happening at cetain points on the graph more easily
amistre64
  • amistre64
it appears that the graph touches then turns at x = -2 .... which is why it is positive on both sides of it....
amistre64
  • amistre64
so it "crosses" the x axis at 2 and 3 which make it go negative AND less than 0
amistre64
  • amistre64
so your notation would be [x|x is an element of (2,3)} or some such notation
anonymous
  • anonymous
x \[\in \cup\]
amistre64
  • amistre64
I am unclear about the "U" set, its been qwhile since I had to play in set theory :)
anonymous
  • anonymous
Ok, I'm going to go with my gut.
amistre64
  • amistre64
gut going is good :)
anonymous
  • anonymous
thank you for your help

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