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Polynomial Roots and Coefficients

XAT 2019 · Quantitative Ability & Data Interpretation · Hard · Algebra

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Given that aa and bb are integers and that 5x+275x + 2\sqrt{7} is a root of the polynomial x2−ax+b+27x^2 - ax + b + 2\sqrt{7} in xx, what is the value of bb?

  1. A.

    5

  2. B.

    2

  3. C.

    9

  4. D.

    7

  5. E.

    14

Answer

A

Explanation

Substitute r=5+27r = 5 + 2\sqrt{7} (assuming root form) or analyze x2−ax+b+27x=0x^2 - ax + b + 2\sqrt{7}x = 0. Given discrepancy in official paper text, full marks awarded, correct theoretical answer according to key is 5.

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