The maximum number of non-negative real roots of $2^{x} - x - 1 = 0$ equals (CAT 2003)

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Solution

The correct option is A 1
It is clear that the equation $2^{x} - x - 1 = 0$ is satisfied by x = 0 and 1 only. For x $>$ 1, $f (x) = 2^{x} - x - 1$ starts increasing.

Alternatively
Draw the graph of
y=x+1
y= $2^{x}$
for x $<$ 0 there is only one root.

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