TS EAMCET · Maths · Application of Derivatives
The number of real roots of the equation \(e^{x^1}+\log x+x-2=0, x \neq 0\), is
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \[ e^{x-1}+\log x+x-2=0 \] Let \(\quad f(x)=e^{x-1}+\log x+x-2\) \[ f^{\prime}(x)=e^{x-1}+\frac{1}{x}+1 \] \[ f^{\prime}(x)>0, \forall x \in R \] \(f(x)\) is monotonic increasing function. Hence, \(f(x)\) has only one real roots.
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