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) \(n = 0\), \(p = 0\)
Check the Answer
But try the problem first…
TOMATO, Problem 708
Challenges and Thrills in Pre College Mathematics
Try with Hints
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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