Let α, β in N be roots of equation x 2 -70 x+λ=0 , where λ/2, λ/3 notin N . If λ assumes the minimum possible value, then frac (√(α-1)+√(β-1))(λ+35) α-β is equal to :

Mathematics · Quadratic Equations

JEE Main 2024 — 30 January, Shift 1 — Question 28

Let $\alpha, \beta \in N$ be roots of equation $x^{2}-70 x+\lambda=0$ , where $\frac{\lambda}{2}, \frac{\lambda}{3} \notin \mathrm{~N}$ . If $\lambda$ assumes the minimum possible value, then $\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|}$ is equal to :

Answer: 60

Numerical answer — enter this value.

Step-by-step solution

$x^{2}-70 x+\lambda=0$

$\alpha+\beta=70$

$\alpha \beta=\lambda$

$\therefore \alpha(70-\alpha)=\lambda$

Since, 2 and 3 does not divide $\lambda$

\therefore \alpha=5, \beta=65, \lambda=325

By putting value of $\alpha, \beta, \lambda$

we get the required value 60 .

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 30 January, Shift 1
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Theory of Quadratic Equations