Question:
The number of real roots of the equation
\[
e^{x-1}+x-2=0
\]
is
The number of real roots of the equation
\[
e^{x-1}+x-2=0
\]
is
Show Hint
Check monotonicity using derivative.
Updated On: Mar 23, 2026
- \(1\)
- \(2\)
- \(3\)
- \(4\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Let \(f(x)=e^{x-1}+x-2\).
Step 2: \[ f'(x)=e^{x-1}+1 > 0 \] ⇒ function is strictly increasing.
Step 3: \[ f(0) < 0,\quad f(1)=0,\quad f(2) > 0 \]
Step 4: Hence two real roots.
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