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)