Explanation

This uses Vieta's formulas for x² + px + q = 0: the sum of the roots is −p and the product is q. Here the roots are p and q themselves, so p + q = −p (i.e. q = −2p) and pq = q. Since q ≠ 0, dividing the product relation by q gives p = 1. Substituting back, q = −2(1) = −2. Hence option (a), (1, −2). The distractor (1, 2) keeps the correct p but assigns the wrong sign to q, and (−1, 2)/(−1, −2) fail the sum-of-roots condition.