Try this beautiful problem on Negative & Positive Roots, useful for ISI B.Stat Entrance.
If n stands for the number of negative roots and p for the number of positive roots of the equation \(e^x = x\), then
Calculus
Limit
Trigonometry
Answer: (d)
TOMATO, Problem 708
Challenges and Thrills in Pre College Mathematics
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 ..........
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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