A question can be really difficult one, but the answer need not be that difficult. Lets see a question which I hope shall use each inch of your brain and yet you shall be amazed to see the solution.
If 2a + 3b + 6c =0, & a,b,c ε R, then prove that a.(x)^2 + b.x + c has atleast one root in
the interval (0,1).
The solution for the same can be found here....