If the sum of all the roots of the equation e²ˣ - 11eˣ - 45e⁻ˣ + 81/2 = 0 is log e p, then p is equal to _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jun, Morning shift · Q44

JEE Main 202227 Jun, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If the sum of all the roots of the equation

{e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0

{\log _e}p

, then p is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 · 27 Jun, Morning shift · Q44

JEE Main 202227 Jun, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If the sum of all the roots of the equation

{e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0

{\log _e}p

, then p is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.