Any help would be greatly appreciated. I am ok with parts i and ii of this question, but part iii is really driving me crazy.
Given that
X^2 +4x +c = (x + a )^2 + b
Where a, b and c are constants
(i) Find the value of a
x^2 +4x +c = (x + a )^2 + b = x^2 + 2ax + a^2 + b
Gathering together like terms,
4x = 2ax
Therefore
4 = 2a
Therefore
a = 2
(ii) Find b in terms of c
c = a^2 + b = 2x2 +b = 4 + b
therefore
c -4 = b
And here is the bit that I am stuck on......
(iii) Given also that the equation X^2 +4x +c = 0 has unequal real roots, find the range of possible values of c.
The answer is c < 4, but I have no idea how that was arrived at