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)

Source
Suggested Reading

TOMATO, Problem 708

Challenges and Thrills in Pre College Mathematics

Try with Hints


First hint

Negative & Positive Roots- graph

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

Negative & Positive Roots - graph

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…..

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