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)