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

## Check the Answer

But try the problem first…

Answer: (d)

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…..

## Other useful links

- https://www.cheenta.com/problem-on-calculus-isi-b-stat-objective-problem-696/
- https://www.youtube.com/watch?v=TRf4TgrOIpA

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