The standard form for a quadratic equation is:
ax2+bx+c=0
where x is the independent variable and a,b,andc are constants.
The discriminant is:
d=√b2−4(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 a2+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=√b2−4(k)(c)
Substitute the coefficients of the given equation, k=1,b=4andc=4:
d=√42−4(1)(4)
d=0
This is the case where the equation is a perfect square, therefore, there is only one real root.
