If we integrate the given expression,i.e. 3ax²+2bx+c we get ax³+bx²+cx

applying limits frm 0 to 2 we find that the value of integeral is 2(4a+2b+c) which is 0

this means that the area under curve of the given expression is 0 b/w 0and2 so the curve of the given expression will have to intersect the x axis in this interval.....so there will be a root in the interval     (0,2)

ans is (c)