Question

Tell how many solutions the equation has. $$ 4 x^{2}+4 x+1=0 $$

Short answer

The given equation has 1 real solution.

Step-by-step solution

Identify coefficients

First, identify the coefficients in the given quadratic equation, which is in the standard form \( ax^2+bx+c=0 \). Here, a = 4, b = 4, and c = 1.

Calculate the discriminant

The number of solutions depends on the discriminant, which is calculated by the formula \( b^2-4ac \). Substituting the identified values, we get \( 4^2 - 4 * 4 * 1 = 16 - 16 = 0 \).

Analyze the discriminant value

The discriminant value is 0. This means the given quadratic equation has exactly one real solution.