MCQMediumJEE Main 2024 · 31 January, Shift 1Nature of Roots & Formation of Equations

Mathematics Question from JEE Main 2024 · 31 January, Shift 1

For 0<c<b<a0 < c < b < a, let (a+b−2c)x2+(b+c−2a)x+(c+a−2b)=0(a + b - 2c)x^2 + (b + c - 2a)x + (c + a - 2b) = 0 and α≠1\alpha \ne 1 be one of its roots. Then, among the two statements

(I) If α∈(−1,0)\alpha \in (-1, 0), then bb cannot be the geometric mean of aa and cc

(II) If α∈(0,1)\alpha \in (0, 1), then bb may be the geometric mean of aa and cc

which of the following is true?

  • A

    Both (I) and (II) are true

  • B

    Neither (I) nor (II) is true

  • C

    Only (I) is true

  • D

    Only (II) is true

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