2022 · Q7
If (x + k) is the HCF of x² + px + q and x² + qx + p, where p ≠ q, then what is the value of k?
Elementary MathematicsHCF and LCM
- A-1
- B0
- C1/2
- D1
Explanation
Subtracting the two quadratics gives (p−q)x + (q−p) = (p−q)(x−1), so any common divisor divides x−1 (since p ≠ q). Hence the linear HCF is x−1 = x+k, giving k = −1. The keyed option is A.