Question

Use the discriminant to describe the roots of each equation. Then select the best description.

Answer 1

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