Limit of Quadratic Roots (Jee Mains)

Evaluation of Limits

Hard

Limit of Quadratic Roots

For t > –1, let α_t and β_t be the roots of the equation $\left( {{{\left( {t + 2} \right)}^{\frac{1}{7}}} - 1} \right){x^2} + \left( {{{\left( {t + 2} \right)}^{\frac{1}{6}}} - 1} \right)x + \left( {{{\left( {t + 2} \right)}^{\frac{1}{{21}}}} - 1} \right) = 0$ . If $\mathop {\lim }\limits_{t \to - {1^ + }} {\alpha _t} = a$ and $\mathop {\lim }\limits_{t \to - {1^ + }} {\beta _t} = b$ , then 72(a+b)² is equal to _____.

Ask about this question