Let be the length of three sides of a triangle satisfying the condition

MATHEMATICS · Subjective · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Let a,b,ca, b, c be the length of three sides of a triangle satisfying the condition (a2+b2)x2−2b(a+c)⋅x+(b2+c2)=0(a^2 + b^2)x^2 - 2b(a + c) \cdot x + (b^2 + c^2) = 0 . If the set of all possible values of xx is the interval (α,β)(\alpha, \beta) , then 12(α2+β2)12(\alpha^2 + \beta^2) is equal to:

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