JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of all the real roots of the equation \(\left( e ^{2 x }-4\right)\left(6 e ^{2 x }-5 e ^{ x }+1\right)=0\) is
- A \(\log _{ c } 3\)
- B \(-\log _{e} 3\)
- C \(\log _{ e } 6\)
- D \(-\log _{e} 6\)
Answer & Solution
Correct Answer
(B) \(-\log _{e} 3\)
Step-by-step Solution
Detailed explanation
\(\left( e ^{2 x}-4\right)\left(6 e ^{2 x }-3 e ^{ x }-2 e ^{ x }+1\right)=0\) \(\left( e ^{2 x }-4\right)\left(3 e ^{ x }-1\right)\left(2 e ^{ x }-1\right)=0\) \(e ^{2 x }=4 \text { or }^{ x }=\frac{1}{3} \text { or }^{ x }=\frac{1}{2}\)…
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