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If α & β be the roots of ax 2 +bx+c = 0, then lim x→α ( 1+ax 2 +bx+c) 1/(x-α) is :-

If α & β be the roots of ax2+bx+c = 0, then limx→α( 1+ax2+bx+c)1/(x-α) is :-

Grade:Upto college level

1 Answers

Anurag Kishore
37 Points
11 years ago

Hi

As α and β are roots

so,

ax2 + bx + c = a(x - α) (x - β)

Let

y = limx->α {1+ a(x - α)(x - β)}1/(x - α)

 

=> log y = limx->α log [1+ a (x - α)(x - β)] / (x - α)

            = limx->α [a(x - α) + a (x - β)] / 1+a(x - β)(x-α)

             = a(α - β)

=> y = ea(α - β)

 

Thanks

Anurag Kishore

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