CDS 2025 · PYQ · Quadratic Equations / Common Roots · medium
The equations x² + px + q = 0 and x² + qx + p = 0 (p ≠ q) have a common root. What is the value of (p + q)?
A.−1✓ Correct
B.0
C.1
D.2
Explanation
Subtracting the two equations: (p−q)x + (q−p) = 0, so (p−q)(x−1) = 0. Since p ≠ q, x = 1 is the common root. Substituting into x² + px + q = 0: 1 + p + q = 0, so p + q = −1.
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