Solve x² − 5x + 6 = 0

Step-by-step solution

1. Step 1: Identify coefficients

   a = 1, b = −5, c = 6.

2. Step 2: Discriminant

   Δ = b² − 4ac = 25 − 24 = 1.

   $$\Delta =1$$

3. Step 3: Quadratic formula

   x = (5 ± 1) / 2, which gives 3 and 2.

   $$x=\frac{5\pm 1}{2}$$

Why this works

A quadratic equation has degree 2. After writing ax² + bx + c = 0, the discriminant tells you how many real roots exist. Here Δ = 1 > 0, so two distinct real roots. Factoring as (x − 2)(x − 3) = 0 produces the same pair.