JEE Main202227 Jun 2022Morning ShiftMathematicsApplication of DerivativesActual

If the sum of all the roots of the equation e 2 x - 11 e x - 45 e - x + 81 2 = 0 is log e P , then P is equal to _____.

Correct answer

Step-by-step solution

Given e 2 x - 11 e x - 45 e x + 81 2 = 0 e 3 x - 11 e 2 x + 81 2 e x - 45 = 0 Let e x = t , so t 3 - 11 t 2 + 81 2 t - 45 = 0 Product of roots t 1 t 2 t 3 = 45 i.e. e x 1 × e x 2 × e x 3 = 45 e x 1 + x 2 + x 3 = 45 x 1 + x 2 + x 3 = log 2 45 Given sum of root = ln P So P = 45

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