If (x-k) is the HCF of x^{2}+ax+b and x^{2}+cx+d, then what is the value of k?
- A. \frac{d-b}{c-a}
- B. \frac{d-b}{a-c} ✓
- C. \frac{d+b}{c+a}
- D. \frac{d-b}{c+a}
Correct Answer: B. \frac{d-b}{a-c}
Explanation
Since (x-k) is the HCF, k must be a root of both equations. So, k^2+ak+b=0 and k^2+ck+d=0. Subtracting the second from the first gives k(a-c) + (b-d) = 0, which yields k = \frac{d-b}{a-c}.
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