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JEE Advanced Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Advanced

If ; are three quadratic equations of which each pair has exactly one root common then the number of solutions of the triplet is

Answer: (A)

Solution

The equations are

:\ -+1=0, :\ -+2=0, :\ -+3=0.

Intended configuration: the common roots of the three pairs are different, i.e. has roots ; has ; has . Products of roots give

αβ=1, αγ=2, β

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Question ID VK-107980