factorize x^2-7x+12 — step-by-step solution

Let's factor in

ℝ

x^{2} - 7 x + 12

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-7)}^{2} - 4 \cdot 1 \cdot 12

Δ = 49 - 4 \cdot 12

Δ = 49 - 48

Δ = 1

Δ > 0

, the equation has two solutions:

Solution first:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{7 - 1}{2}

x1 = \frac{6}{2}

x1 = 3

For the 2nd solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{7 + 1}{2}

x2 = \frac{8}{2}

x2 = 4

▷Result: $(x - 3) \cdot (x - 4)$