Find the values of m which make the following quadratic function a perfect square. x2 + 2(m + 1)x + m + 3

Find the values of m which make the following quadratic function a perfect square. x2 + 2(m + 1)x + m + 3

Answer Details

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