Let α, β be the roots of the quadratic equation 12 x 2 -20 x +3 λ=0, λ in mathbb Z . If 1/2 leq β-α leq 3/2 , then the sum of all possible values of λ is :

Mathematics · Quadratic Equations

JEE Main 2026 — 22 January, Evening Shift — Question 13

Let $\alpha, \beta$ be the roots of the quadratic equation $12 \mathrm{x}^{2}-20 \mathrm{x}+3 \lambda=0, \lambda \in \mathbb{Z}$ . If $\frac{1}{2} \leq|\beta-\alpha| \leq \frac{3}{2}$ , then the sum of all possible values of $\lambda$ is :

Option A:
$6$
Option B:
$1$
Option C:
$3$
Correct
Option D:
$4$

Answer: C

Step-by-step solution

$\quad \frac{1}{2} \leq|\alpha-\beta| \leq \frac{3}{2}$

$\frac{1}{4} \leq|\alpha-\beta|^{2} \leq \frac{9}{4}$

$\frac{1}{4} \leq(\alpha+\beta)^{2}-4 \alpha \beta \leq \frac{9}{4}$

$\frac{1}{4} \leq \frac{25}{9}-4 \times \frac{\lambda}{4} \leq \frac{9}{4}$

$-\frac{91}{36} \leq-\lambda \leq \frac{-19}{36}$

$\frac{19}{36} \leq \lambda \leq \frac{91}{36}$

$\lambda=1,2$

Sum $=3$

Answer key and solution verified before publishing.

Practise Quadratic Equations

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 22 January, Evening Shift
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots of Quadratic Equation