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Black Book Advanced Problems in MathematicsMathematicsQuadratic Equation

Let a, b, c be the lengths of the sides of a triangle (no two of them are equal) and k R . If the roots of the equation x^2 + 2(a+b+c)x + 6k(ab+bc+ca) = 0 are real, then:

Options

Ak < 2/3
Bk > 2/3
Ck > 1
Dk < 1/4 .

Correct answer

A. k < 2/3

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