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Cubic Polynomial Coefficient

XAT 2014 · Quantitative Ability & Data Interpretation · Medium · Algebra

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A polynomial y=ax3+bx2+cx+dy = ax^3 + bx^2 + cx + d intersects x-axis at 1 and -1, and y-axis at 2. The value of b is:

  1. A.

    -2

  2. B.

    0

  3. C.

    1

  4. D.

    2

  5. E.

    Cannot be determined

Answer

A

Explanation

At (0,2)  ⟹  d=2(0, 2) \implies d = 2. At (1,0)  ⟹  a+b+c+2=0(1, 0) \implies a + b + c + 2 = 0. At (−1,0)  ⟹  −a+b−c+2=0(-1, 0) \implies -a + b - c + 2 = 0. Adding the two equations: 2b+4=0  ⟹  b=−22b + 4 = 0 \implies b = -2.

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