71How did you do Aditya?
I'm getting m = 2,3 , infact m ε [2,3] , but I won't bid for the latter.
\hspace{-16}$The Value of $\mathbf{m}$ for Which the equations\\\\ $\mathbf{(5m-m^2)^2.\sin^2 x-10.\sin x.(5m-m^2)+24=0}$\\\\ Has exactly $\mathbf{\underline{\bold{Three}}}$ Solution in $\mathbf{[0,2\pi].}$
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8 Answers
71
1im getting no value of m.
solving using quadratic formula we get sinx = 65m-m2 , 45m-m2
note that from the graph of sinx it is clear that only for sinx = 0 we have 3 solutions in [0,2pi]
but both the expressions can't be zero.
36ya for m being a real no. there's no defined soln for it...
as D ≥ 0 (always) and three solns are possible only when sin x = 0 so, no soln...!!
262we can have 3 solns. if (sinx =1 or -1) and (sinx =c where -1<c<1)
36no when sinx = 1 or -1 then pi/2 and 3pi/2 are the only two solns. between 0 and 2pi.!!
and there's a difference in the two statements....
"can have three solutions" and, "exactly three solns"...!!
71@Rishabh Three roots do exist exactly in [0,2Î ]
See the image below for m =3, similar is for m =2.
@Aditya, for the values you gave, the 3 roots lie in [-2Î , 0] while only one in the asked range.
See here
