Question

The number of real roots of e^x = x^2 is/are
(A) 0 (B) 1 (C) 2 (D) 3.

Solution

Many have solved it using graph, but for a complex problem that may not be feasible.

So let us look at another way of finding the solution.

Consider the function f(x)=e^x-x^2

Here f'(x)=e^x-2x>0 forall x in R, so f(x) will have atmost 1 root.

f(-oo)<0, f(0)>0, f is continuos so there is one root of f between (-oo,0).