Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 : a ≠ 0, then
The nature of it's roots can be determined by the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
For x² - 4x + 4 = 0 ← in standard form
with a = 1, b = - 4, c = 4, then
b² - 4ac = (- 4)² - (4 × 1 × 4) = 16 - 16 = 0
Hence roots are real and equal
This can be shown by solving the equation
x² - 4x + 4 = 0
(x - 2)² = 0
(x - 2)(x - 2) = 0, hence
x - 2 = 0 or x - 2 = 0
x = 2 or x = 2 ← roots are real and equal
