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MCQHardJEE Main 2023 · 29 January, Shift 1Nature of Roots & Formation of Equations

Mathematics Question from JEE Main 2023 · 29 January, Shift 1

Let λ≠0\lambda \ne 0 be a real number. Let α,β\alpha, \beta be the roots of the equation

14x2−31x+3λ=014x^2 - 31x + 3\lambda = 0

and α,γ\alpha, \gamma be the roots of the equation

35x2−53x+4λ=0.35x^2 - 53x + 4\lambda = 0.

Then 3αβ\frac{3\alpha}{\beta} and 4αγ\frac{4\alpha}{\gamma} are the roots of the equation:

  • A

    7x2+245x−250=07x^2 + 245x - 250 = 0

  • B

    7x2−245x+250=07x^2 - 245x + 250 = 0

  • C

    49x2−245x+250=049x^2 - 245x + 250 = 0

  • D

    49x2+245x+250=049x^2 + 245x + 250 = 0

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