Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the
FURTHER MATHEMATICS
WAEC 2015
Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.
- A. k = 5, r = -1
- B. k = 5, r = 2
- C. k = 2, r = -5
- D. k = -1, r = 5
Correct Answer: B. k = 5, r = 2
Explanation
\(x^{2} + 4x + k = (x + r)^{2} + 1\)
\(x^{2} + 4x + k = x^{2} + 2rx + r^{2} + 1\)
Comparing the LHS and RHS equations, we have
\(2r = 4 \implies r = 2\)
\(k = r^{2} + 1 = 2^{2} + 1 = 5\)
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