JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of real roots of the equation \(\mathrm{e}^{4 \mathrm{x}}-\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}-\mathrm{e}^{\mathrm{x}}+1=0\) is equal to \(.....\)
- A \(7\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(t^{4}-t^{3}-4 t^{2}-t+1=0, e^{x}=t>0\) \(\Rightarrow t^{2}-t-4-\frac{1}{t}+\frac{1}{t^{2}}=0\) \(\Rightarrow \alpha^{2}-\alpha-6=0, \alpha=t+\frac{1}{t} \geq 2\) \(\Rightarrow \alpha=3,-2(\text { reject })\) \(\Rightarrow t+\frac{1}{t}=3\) \(\Rightarrow\) The number of real…
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