For 12x2−20x+3λ=0: α+β=35, αβ=4λ.
∣β−α∣=325−9λ
Given 21≤325−9λ≤23
49≤25−9λ≤481
From left: λ≤3691≈2.53
From right: λ≥3619≈0.53
Since λ∈Z: λ∈{1,2}. Sum =3.
Let α,β be the roots of the quadratic equation 12x2−20x+3λ=0,λ∈Z. If 21⩽∣β−α∣⩽23, then the sum of all possible values of λ is :
Held on 22 Jan 2026 · Verified 6 Jul 2026.
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