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MCQMediumJEE Main 2023 · 30 January, Shift 2Solving Linear Equations (Matrix Method)

Mathematics Question from JEE Main 2023 · 30 January, Shift 2

For α,β∈R\alpha, \beta \in \mathbb{R}, suppose the system of linear equations

x−y+z=5x - y + z = 5 2x+2y+αz=82x + 2y + \alpha z = 8 3x−y+4z=β3x - y + 4z = \beta

has infinitely many solutions. Then α\alpha and β\beta are the roots of:

  • A

    x2−10x+16=0x^2 - 10x + 16 = 0

  • B

    x2+18x+56=0x^2 + 18x + 56 = 0

  • C

    x2−18x+56=0x^2 - 18x + 56 = 0

  • D

    x2+14x+24=0x^2 + 14x + 24 = 0

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