Question

If \( \alpha \) and \( \beta \) (\( \alpha<\beta \)) are the roots of the equation \( (-2 + \sqrt{3})(\sqrt{x} - 3) + (x - 6\sqrt{x}) + (9 - 2\sqrt{3}) = 0 \), \( x \ge 0 \), then \( \sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta} \) is equal to:

• A. 8
• B. 11
• C. 9
• D. 10

Hint:

If the roots are \( \sqrt{\alpha} \) and \( \sqrt{\beta} \), then \( \sqrt{\alpha\beta} \) is simply the product of the roots of the quadratic in \( t \).

Answer 1

The Correct Option is C