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.
