What is the discriminant of the quadratic equation x² - 4x + 4 = 0?

To find the discriminant of the quadratic equation given by the standard form ( ax^2 + bx + c = 0 ), we can use the formula for the discriminant, which is ( D = b^2 - 4ac ).

In the quadratic equation ( x^2 - 4x + 4 = 0 ), the coefficients are:

• ( a = 1 )

• ( b = -4 )

• ( c = 4 )

Substituting these values into the discriminant formula gives:

[

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

]

Calculating this step-by-step:

1. Calculate ( (-4)^2 = 16 ).

2. Calculate ( 4(1)(4) = 16 ).

3. Now substitute back into the formula: ( D = 16 - 16 = 0 ).

A discriminant of 0 indicates that the quadratic equation has exactly one real solution (or a repeated real root), which arises from the fact that the quadratic touches the x-axis at one point. Thus, the correct answer is 0, as it signifies a perfect square trinomial in this case, confirming that the