factorize x^2-5x+6 — step-by-step solution

Let's factorize in

ℝ

x^{2} - 5 x + 6

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-5)}^{2} - 4 \cdot 1 \cdot 6

Δ = 25 - 4 \cdot 6

Δ = 25 - 24

Δ = 1

Since

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{5 - 1}{2}

x1 = \frac{4}{2}

x1 = 2

Solution 2nd:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{5 + 1}{2}

x2 = \frac{6}{2}

x2 = 3

▷Result: $(x - 2) \cdot (x - 3)$