In this aptitude (simplification and polynomials) question, the cubic polynomial 2x^3 - x^2 - 2x + 1 has zeros a, b, and c. Using the relationship between roots and coefficients for a cubic, determine the value of a + b + c (the sum of the roots).

Introduction / Context:
This problem tests knowledge of standard relationships between the roots and coefficients of a polynomial, specifically a cubic. Instead of explicitly solving for each root, which may be messy, we can directly use the sum of roots formula. This is a powerful shortcut that saves time in aptitude exams and higher mathematics problems involving symmetric expressions in roots.

Given Data / Assumptions:
The cubic polynomial is 2x^3 - x^2 - 2x + 1.
Its zeros (roots) are a, b, and c, which may be real or complex.
We are asked to find a + b + c, the sum of the roots.

Concept / Approach:
For a general cubic equation of the form ax^3 + bx^2 + cx + d = 0 with roots r1, r2, r3, the sum of the roots is given by -b / a. This result comes from comparing coefficients after factoring the polynomial into a(x - r1)(x - r2)(x - r3). We can apply this directly without finding individual roots, provided we correctly identify the coefficients a and b.

Step-by-Step Solution:
Write the polynomial in standard form: 2x^3 - x^2 - 2x + 1 = 0. Here a = 2, b = -1, c = -2, and d = 1. Let the roots be a, b, and c as given in the question statement. By the sum of roots formula for cubics, a + b + c = -b / a. Substitute b = -1 and a = 2: a + b + c = -(-1) / 2. This simplifies to a + b + c = 1 / 2.

Verification / Alternative check:
We can verify the formula quickly by recalling the factorised form for a cubic: 2(x - a)(x - b)(x - c). When we expand this product, the coefficient of x^2 is -2(a + b + c). This must match the given polynomial where the x^2 coefficient is -1. Equating -2(a + b + c) with -1 gives a + b + c = 1 / 2, which confirms the earlier calculation using the standard formula.

Why Other Options Are Wrong:
Option -1/2 would arise from incorrectly using b / a instead of -b / a. Option 1 and option -1 correspond to errors in equating coefficients, for example mismatching the factor 2 from the leading coefficient. Option 0 would imply that the x^2 coefficient is zero, which is not the case. Therefore only 1/2 is consistent with the actual polynomial coefficients.

Common Pitfalls:
Learners sometimes confuse formulas for sum of roots of quadratic and cubic equations or forget to divide by the leading coefficient. Another common error is to misread the sign of the x^2 coefficient. To avoid mistakes, always rewrite the polynomial in standard form and clearly label a, b, c, and d before applying the formula for the sum of roots.

Final Answer:
The sum of the zeros a, b, and c of the polynomial 2x^3 - x^2 - 2x + 1 is 1/2.