Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $(\sqrt[3]{(1+a)}-1) x^2+(\sqrt{(1+a)}-1) x+(\sqrt[6]{(1+a)}-1)=0$ where $a>-1$, then $\mathop {\lim }\limits_{a \to {0^ + }} \alpha (a)$ and $\mathop {\lim }\limits_{a \to {0^ + }} \beta (a)$, are

$\left(-\frac{5}{2}\right)$ and 1

$\left(-\frac{7}{2}\right)$ and 2

$\left(-\frac{9}{2}\right)$ and 3

JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

\alpha(a)

and

\beta(a)

be the roots of the equation

(\sqrt[3]{(1+a)}-1) x^2+(\sqrt{(1+a)}-1) x+(\sqrt[6]{(1+a)}-1)=0

where

a>-1

, then

\lim\limits_{a \to {0^ + }} \alpha (a)

and

\lim\limits_{a \to {0^ + }} \beta (a)

, are

View answer and explanation

Correct option: B

\left(-\frac{1}{2}\right)

and

(-1)

Option B (

\left(-\frac{1}{2}\right)

and

(-1)

) is correct because after applying L'Hopital's rule and simplifying, the roots of the resulting quadratic equation are -1/2 and -1.