If $p, q$ are the distinct roots of the equation $x^2 + px + q = 0$, then
- $p = 1, q = -2$
- $p = 0, q = 1$
- $p = -2, q = 0$
- $p = -2, q = 1$
Reveal answer
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A
Correct answer
Explanation
For x^2 + px + q = 0, the sum of roots p + q = -p (so 2p + q = 0) and the product of roots p*q = q. If q is not 0, then p = 1. Substituting p = 1 into 2p + q = 0 gives q = -2. Thus, p = 1 and q = -2.
AI explanation
Since p and q are roots of x^2 + px + q = 0, substituting x = p gives p^2 + p^2 + q = 0, so 2p^2 + q = 0. Substituting x = q gives q^2 + pq + q = 0, which factors to (q+1)(q+p) = 0. Testing q = -1 in the first equation yields p = 1 or p = -1, but the roots must be distinct so p cannot equal q. Testing q = -p in the first equation gives 2p^2 - p = 0, which yields the distinct pair p = 1 and q = -2. The values are p = 1, q = -2.