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let α and β be the distinct roots of ax2+bx+c=0 then limx→α1−cos(ax2+bx+c)/(x−α)^2 is equal to?

let α and β be the distinct roots of ax2+bx+c=0 then limx→α1−cos(ax2+bx+c)/(x−α)^2 is equal to?

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
Since α,β are the roots of ax2+bx+c=0
limx→α   (1−cos(x−α)(x−β)) / (x−α)2
⇒limx=α 2sin2(x−α)(x−β)2a2(x−α)2(x−β)24×a2(x−α)2(x−β)24(x−α)2
 
⇒limx=α {(2sin2(x−α)(x−β) / 2)  / ( a2(x−α)2(x−β)2 / 4) } × {a2(x−α)2(x−β)2 / 4(x−α)2 }
 
⇒2×a2(α−β)2 / 4
 
⇒a2(α−β)2 /2

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