InterviewSolution
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InterviewSolution
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`e^(|sinx|)+e^(-|sinx|)+4a=0`will have exactly four different solutions in `[0,2pi]`if.`a in R`(b) `a in [-3/4,-1/4]``a in [(-1-e^2)/(4e),oo]`(d) none of theseA. `a in [-(e)/(4),-(1)/(4)]`B. `a in R`C. `a in [-(-1-e^(2))/(4e),oo)`D. none of these |
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Answer» Correct Answer - D Let `t = e^(|sin x|) "Clearly", t in [1, e]`. `therefore" "e^(|sin x|)+e^(-|sin x|) + 4a = 0` `rArr" "t^(2) + 4at + 1 = 0 or f(t) = 0, "where" f(t) = t^(2) + 4at + 1` This will have two distinct real roots in [1, e], if `f(1) gt 0, f(e) gt 0, 1 lt -2a lt e and 16 a^(2) - 4 gt 0` `rArr" "4a+2 gt 0, e^(23)+4ae + 1 gt 0, -(e)/(2)lt a lt (-1)/(2) and a lt (-1)/(2) or a gt (1)/(2)` `rArr" "a gt (-1)/(2), a gt -(1+e^(2))/(4e), -(e)/(2) lt a lt (-1)/(2) and a lt (-1)/(2) or a gt (1)/(2)` Clearly, there is no value of a satisfying the above in equalities. |
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