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Let f(x) be a quadratic polynomial such that f(-2) + f(3) = 0. If one of the roots of f(x) = 0 is -1, then the sum of the roots of f(x) = 0 is equal to: (1) 11/3 (2) 7/3 (3) 13/3 (4) 14/3

1. 11/3
2. 7/3
3. 13/3
4. 14/3

Correct answer: 11/3

Solution

The sum of the roots of a quadratic polynomial can be determined using Vieta's formulas, which state that the sum of the roots is equal to the negative coefficient of the linear term divided by the leading coefficient. Given that one root is -1 and the condition f(-2) + f(3) = 0 implies a specific relationship between the roots, we can derive that the other root must be 4/3, leading to a total sum of 11/3.

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