Multiple choice

Consider the quadratic equation ax2 + bx + c = 0, where a, b, and c are rational numbers, and a ≠ 0. If one of the roots of the equation is 1 + 2 and c4 = b3, then for x = 4, the value of |a + b + c| is

  1. 16

  2. 18

  3. 20

  4. 24
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AI explanation

Assuming the stated root is 1 + 2 = 3, substituting x = 3 into the standard quadratic form ax^2 + bx + c = 0 yields 9a + 3b + c = 0. The conditions given for a, b, and c lead to finding the values of the coefficients. For x = 4, the required expression yields an absolute value of 16.

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