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  • Solve this problem - Complex numbers and quadratic equations - JEE Main-8

The equation e^{\sin x}-e^{-\sin x}-4=0 has

  • Option 1)

    infinite number of real roots

  • Option 2)

    no real roots

  • Option 3)

    exactly one real root

  • Option 4)

    exactly four real roots

 

Answers (2)

best_answer

e^{\sin x}-e^{-\sin x}-4= 0

\left ( e^{\sin x} \right )^{2}-4e^{\sin x}-1= 0\Rightarrow t^{2}-4t-1= 0

\Rightarrow t= \frac{4\pm \sqrt{16+4}}{2}= 2\pm \sqrt{5}

i.e.,e^{\sin x}= 2+\sqrt{5}\: or  

\sin x= ln\left ( 2+\sqrt{5} \right )> 1\therefore No \, real \, root


Option 1)

infinite number of real roots

Option 2)

no real roots

Option 3)

exactly one real root

Option 4)

exactly four real roots

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