Quadratic Equation Question 5
Question 5 - 2024 (30 Jan Shift 1)
Let $\alpha, \beta \in \mathrm{N}$ be roots of equation $\mathrm{x}^{2}-70 \mathrm{x}+\lambda=0$, where $\frac{\lambda}{2}, \frac{\lambda}{3} \notin \mathrm{N}$. If $\lambda$ assumes the minimum possible
nan
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Answer (60)
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 .
