Find the values of m which make the following quadratic function a perfect square. x2 + 2(m + 1)x + m + 3
-
A.
-1, 1 -
B.
-1, 2 -
C.
1, -2 -
D.
2, -2
Correct Answer: Option C
Explanation
x2 + 2(m + 1)x + m + 3 from (A + B)2 = a2 + 2AB + b2
2B = (frac{2(m + 1)}{2}) = m + 1 …….(i)
Also B2 = m + 3……….(ii)
Subst. for B in equation ……….(iii)
= (m + 1)2 = m + 3 = m2 + 2m + 1 = m + 3
= m2 + 2m – m + 1 – 3 = 0
m2 + m – 2 = 0
(m + 2)(m – 1) = 0 or m – 1 = 0
m = -2 or 1