Question:
Let \( \alpha(a) \) and \( \beta(a) \) be the roots of the equation <span class="math-display">\[ \left( \sqrt{1 + a} - 1 \right)x^2 + \left( \sqrt{1 + a} - 1 \right)x + \left( \sqrt{1 + a} - 1 \right) = 0 \] where \( a > -1 \). Then \( \lim_{a \to -0} \alpha(a) \) and \( \lim_{a \to -0} \beta(a) \) are
-\frac{5}{2} and 1
-\frac{1}{2} and -1
\frac{7}{2} and 2
-\frac{9}{2} and 3
Step-by-Step Solution
(as we are getting two f images for one x in the domain)
Correct Answer: (zero marks to all)