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
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #31899)