What is the value of α(α≠0) for which x^2-5x+\alpha and x^2-7x+2\alpha have a common factor ? [2017 CDS-II]

UPSC 2017 CDS II Math Paper

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What is the value of α(α≠0) for which x2−5x+α and x2−7x+2α have a common factor ?

[2017 CDS-II]

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