2021 · Q84
If (x − k) is the HCF of x² + ax + b and x² + cx + d, then what is the value of k?
Elementary MathematicsAlgebra
- A(d−b)/(c−a)
- B(d−b)/(a−c)
- C(d+b)/(c+a)
- D(d−b)/(c+a)
Explanation
Since x = k is a common root, k² + ak + b = 0 and k² + ck + d = 0. Subtracting: (a−c)k = d − b, so k = (d−b)/(a−c). Hence option B.