Number of roots of equation

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)!!.

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