JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \( \alpha, \beta \) be the roots of the quadratic equation \( 12x^{2}-20x+3\lambda=0, \lambda\in\mathbb{Z} \). If \( \frac{1}{2}\le|\beta-\alpha|\le\frac{3}{2}, \) then the sum of all possible values of \( \lambda \) is :
- A 6
- B 1
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(\frac{1}{2} \leq|\alpha-\beta| \leq \frac{3}{2}\) \(\frac{1}{4} \leq|\alpha-\beta|^2 \leq \frac{9}{4}\) \(\frac{1}{4} \leq(\alpha+\beta)^2-4 \alpha \beta \leq \frac{9}{4}\) \(\frac{1}{4} \leq \frac{25}{9}-4 \times \frac{\lambda}{4} \leq \frac{9}{4}\)…
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