If … are the roots of the equation …, and … :

Option D. Since, … are roots of …

Limits Continuity and Differentiability

JEE Main 2023 · 8 Apr, Evening shift · Q4299

MathematicsHard179×since 2002Q4299

\alpha > \beta > 0

are the roots of the equation

a x^{2}+b x+1=0

, and

\lim_\limits{x \rightarrow \frac{1}{\alpha}}\left(\frac{1-\cos \left(x^{2}+b x+a\right)}{2(1-\alpha x)^{2}}\right)^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right), \text { then } \mathrm{k} \text { is equal to }

JEE Main 2023 · 8 Apr, Evening shift · Q4299

MathematicsHard179×since 2002Q4299

\alpha > \beta > 0

are the roots of the equation

a x^{2}+b x+1=0

, and

\lim_\limits{x \rightarrow \frac{1}{\alpha}}\left(\frac{1-\cos \left(x^{2}+b x+a\right)}{2(1-\alpha x)^{2}}\right)^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right), \text { then } \mathrm{k} \text { is equal to }