JEE Mains · Maths · STD 12 - 6. Application of derivatives
The number of real roots of the equation \(e^{6 x}-e^{4 x}-2 e^{3 x}-12 e^{2 x}+e^{x}+1=0\) is:
- A \(1\)
- B \(6\)
- C \(4\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\(e^{6 x}-e^{4 x}-2 e^{3 x}-12 e^{2 x}+e^{x}+1=0\) \(\Rightarrow\left(e^{3 x}-1\right)^{2}-e^{x}\left(e^{3 x}-1\right)=12 e^{2 x}\) \(\left(e^{3 x}-1\right)^{2}\left(e^{x}-e^{-x}-e^{-2 x}\right)=12\)…
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