How do you solve $2x^3+x^2>6x$ using a sign chart?

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How do you solve $2x^3+x^2>6x$ using a sign chart?

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Answer 1 · 2016-10-18T08:56:15

the answer is $-2< x< 0$ and $x>3/2$

Explanation:

We need to factorise the expresson
$2x^3+x^2-6x>0 =>x(2x^2+x-6)>0$
$=>$ $x(2x-3)(x+2)>0$
So the key points we have to look at are $x=0$ $x=3/2$ and $x=-2$

If $x<-2$ the expression is $<0$
If $-2< x< 0$ the expression is $>0$
If $0< x< 3/2$ the expression is $<0$
If $x>3/2$ the expression is $>0$
So the answer is $-2< x< 0$ and $x>3/2$

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How do you solve $2x^3+x^2>6x$ using a sign chart?

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