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
- A \(4\)
- B \(2\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(\mathrm{e}^{4 \mathrm{x}}+\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{x}}+1=0\) Divide by e \(2 x\) \(\Rightarrow \quad \mathrm{e}^{2 \mathrm{x}}+\mathrm{e}^{\mathrm{x}}-4+\frac{1}{\mathrm{e}^{\mathrm{x}}}+\frac{1}{\mathrm{e}^{2 \mathrm{x}}}=0\)…
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