JEE Main 2024 Mathematics question
Let α, β ∈ ℕ be roots of the equation x² – 70x + λ = 0. Where λ/2, λ/3 ∉ ℕ. If λ assumes the minimum possible value, then is equal to :
Answer: 60
Solution
α + β = 70 and αβ = λ. Since λ/2 and λ/3 are not natural numbers, λ is not divisible by 2 or 3, so neither α nor β is divisible by 2 or 3. With λ = α(70 − α) increasing for α ≤ 35, the
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