α and β are distinct real roots of the quadratic equation x² + ax + b = 0. Which of the following statements is/are sufficient to find α? 1. α + β = 0, α² + β² = 2 2. αβ² = -1 and a = 0 Select the correct answer using the code given below:

Statement 1 gives alpha + beta = 0 and alpha2 + beta2 = 2. Using the identity (alpha + beta)2 = alpha2 + beta2 + 2 alpha beta, we get 0 = 2 + 2 alpha beta, so alpha beta = -1. Because the roots are distinct and sum to zero, alpha = 1 and beta = -1, which is sufficient to find alpha. Statement 2 gives a = 0, meaning the sum alpha + beta = 0, so beta = -alpha. Substituting this into alpha beta2 = -1 yields alpha (-alpha)2 = -1, so alpha3 = -1, which means alpha = -1, making statement 2 also sufficient. Therefore, both statements are sufficient.

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