If β, 2,2m are in GP, then what is the value of \beta\sqrtm? [NDA II 2016]

UPSC NDA 2 2016 Mathematics Solved Paper

Consider the following for the next two (02) items that follow:
2x2+3x−α−0 has roots −2 and β while the equation x2−3mx+2m2=0 has both roots positive, where α>0 and β>0

[NDA II 2016]

Question : 40 of 120

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If β, 2,2m are in GP, then what is the value of β√m?

[NDA II 2016]

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