How many solutions does the equation \(x^2 + 4x + 4 = 0\) have?

To determine how many solutions the equation (x^2 + 4x + 4 = 0) has, we can utilize the concept of the discriminant, which is derived from the quadratic formula. The discriminant is given by the expression (D = b^2 - 4ac), where (a), (b), and (c) are the coefficients from the quadratic equation (ax^2 + bx + c = 0).

In this case, the coefficients are:

• (a = 1)

• (b = 4)

• (c = 4)

Now, we calculate the discriminant:

[

D = 4^2 - 4(1)(4) = 16 - 16 = 0

]

When the discriminant (D) is zero, this indicates that there is exactly one real solution to the quadratic equation. This means that the parabola represented by the equation touches the x-axis at a single point, also known as a repeated or double root.

Therefore, the equation (x^2 + 4x + 4 = 0) has precisely one solution, which aligns with the choice indicating