Inequality

Guys please help i have like a whole exercise on these can someone please provide a working answear.

x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to

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Originally Posted by iFuuZe

Guys please help i have like a whole exercise on these can someone please provide a working answear.

x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to

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You need to use brackets where they're needed so we can understand what the inequation actually is.

Is it ?

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Originally Posted by iFuuZe

Guys please help i have like a whole exercise on these can someone please provide a working answear.

x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to

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Inequality is equivalent to the :

yep so you factorice the top and bottom now what we do procede....

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Originally Posted by iFuuZe

yep so you factorice the top and bottom now what we do procede....

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A function will only ever stop being negative at the x intercepts, so evaluate where they are, then test some points between each of them to determine which of the regions give negative values for the function :)

link

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Originally Posted by Prove It

A function will only ever stop being negative at the x intercepts...

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or at a discontinuity. (Nerd)

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Originally Posted by a tutor

or at a discontinuity. (Nerd)

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Let's assume we've already established that :P

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Originally Posted by Prove It

Let's assume we've already established that :P

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Of course.

I'm just pointing out that you can get a sign change at a discontinuity too.

guys i dont understand, its better if i visualise a worked example if any can do that it would fantastic

Sign changes occur whenever the sign of one factor changes.

This will happen at x= -4,-2,-1,1,3 and 5.

So check x<-4. Here all factors <0 so the expression is positive.

x<-4 positive
-4<x<-2 negative
-2<x<-1 positive
-1<x<1 negative
1<x<3 positive
3<x<5 negative
x>5 positive