if a is a repeated root of  ax2+bx+c=0, limx→αsin⁡ax2+bx+c(x−α)2 is equal to

Since  a is a repeated root of ax2+bx+c=0∴ ax2+bx+c=a(x−α)2limx→α sin⁡ax2+bx+c(x−α)2=limx→α sin⁡a(x−α)2(x−α)2=alimx→α sin⁡a(x−α)2a(x−α)2=a×1=a.