JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The equation \(e^{4 x}+8 e^{3 x}+13 e^{2 x}-8 e^x+1=0, x \in R\) has:
- A two solutions and both are negative
- B no solution
- C four solutions two of which are negative
- D two solutions and only one of them is negative
Answer & Solution
Correct Answer
(A) two solutions and both are negative
Step-by-step Solution
Detailed explanation
\(e^{4 x}+8 e^{3 x}+13 e^{2 x}-8 e^x+1=0\) Let \(e^x=t\) Now, \(t^4+8 t^5+13 t^2-8 t+1=0\) Dividing equation by \(t ^2\), \(t^2+8 t+13-\frac{8}{t}+\frac{1}{t^2}=0\) \(t^2+\frac{1}{t^2}+8\left(t-\frac{1}{t}\right)+13=0\)…
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