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Intermediate Value Theorem

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The Intermediate Value Theorem states that on a closed interval [a,b], if there is a value, d, between f(a) and f(b), then there is a point, c, on the interval [a,b] such that f(c) = d.
 
So how does this relate to your problem?  Simple.  In your problem we want to know if there is a value f(x=c) = 0 on the interval.  So compute f(a) and f(b) for each of the candidate intervals and see if f(x)=0 lies between them.  If it does, it's the answer.
 
I'll do A (Between 0 and 1) for you:
 
f(0) = (0)4-3(0)2-8=-8
f(1) = (1)4-3(1)2-8 = 1-3-8 = -10
 
f(x) = 0 does not lie between f(0)=-8 and f(1)=-10, so choice A is not the answer.