If $\alpha $ is a repeated root of $a{x^2} + bx + c = 0$, then $\mathop {\lim }\limits_{x \to \alpha } \frac{{\sin \left( {a{x^2} + bx + c} \right)}}{{{{\left( {x - \alpha } \right)}^2}}}$ is

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

\alpha

is a repeated root of

a{x^2} + bx + c = 0

, then

\lim\limits_{x \to \alpha } \frac{{\sin \left( {a{x^2} + bx + c} \right)}}{{{{\left( {x - \alpha } \right)}^2}}}

View answer and explanation

Correct option: B

a

Option B (

a

) is correct because the limit simplifies to

a

after substituting

a{x^2} + bx + c = a{\left( {x - \alpha } \right)^2}

and applying the limit.

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