The standard form for a quadratic equation is:
ax^2+ bx+c = 0
where x is the independent variable and a, b, and c are constants.
The discriminant is:
d = sqrt(b^2-4(a)(c))
If d < 0 then the quadratic equation has two complex conjugate roots.
If d = 0 then the quadratic equation has one real root (Actually, it indicates that the quadratic is a perfect square and there are two real roots but they are the same value).
If d > 0 then the quadratic equation has to distinct real roots.
Given a^2 + 4a + 4 = 0
Because your equation uses a ask the independent variable, we shall use k for the leading coefficient of the square term:
d = sqrt(b^2-4(k)(c))
Substitute the coefficients of the given equation, k = 1, b=4 and c = 4:
d = sqrt(4^2-4(1)(4)
d = 0
This is the case where the equation is a perfect square, therefore, there is only one real root.
