If α is a repeated root of ax² + bx + c = 0, then Lim_x→α tan(ax² + bx + c) / (x - α)² is ???

Dear Mainak

α is a repeated root of ax² + bx + c = 0

so   ax² + bx + c=a(x-α)²

now  Lim_x→α tan(ax² + bx + c) / (x - α)² 

         =Lim_x→α [tana(x-α)² ]/ (x - α)²

        =Lim_x→α a[tana(x-α)² ]/ a(x - α)²

        =a             because   Lim_x→0 tanx /x   = 1 

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