How would i find the discriminant and what type of solution would it be?

a2+4a+4=0

1 Answer
May 17, 2018

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=b24(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=b24(k)(c)

Substitute the coefficients of the given equation, k=1,b=4andc=4:

d=424(1)(4)

d=0

This is the case where the equation is a perfect square, therefore, there is only one real root.