Let m, n be real numbers. If \alpha is the root of x^2+3 m^2 x+5 n^2=0, \beta is a root of x^2+9 m^2 x+15 n^2=0 and 0< \alpha< \beta, then the equation x^2+6 m^2 x+10 n^2=0, has a root \gamma that always satisfies

CUSAT 2022 BTech Solved Paper Shift 4

Question : 133 of 200

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Let m,n be real numbers. If α is the root of x2+3m2x+5n2=0,β is a root of x2+9m2x+15n2=0 and 0<α<β, then the equation x2+6m2x+10n2=0, has a root γ that always satisfies

γ=‌
α
4
+β
β<γ
α<γ<β
γ=‌
α
2
+β

Validate

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