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Given that (x^{2} + 4x + k = (x + r)^{2} + 1), find the…

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: Option B
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)