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Try this beautiful problem on Negative & Positive Roots, useful for ISI B.Stat Entrance.

## Negative & Positive Roots | ISI B.Stat Entrance | Problem 708

If n stands for the number of negative roots and p for the number of positive roots of the equation $e^x = x$, then

• (a) $n = 1$, $p = 0$
• (b) $n = 0$, $p = 1$
• (c) $n = 0$, $p > 1$
• (d) $n = 0$, $p = 0$

### Key Concepts

Calculus

Limit

Trigonometry

But try the problem first…

Source

TOMATO, Problem 708

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

Draw the figure of given equation $e^x = x$ and check all the points that are in the options…..

Can you now finish the problem ……….

Final Step

The given equation is $e^x = x$

as $x$increases exponential function increases more rapidly than any polynomial function say $x$ . Hence from graph we can say they never intersect . So, there is no solution for the equation . Therefore $n=0$ and $p=0.$

Therefore option $(d)$ is correct…..