The document describes three methods for finding the roots of a quadratic function: factoring, the general formula, and synthetic division or Ruffini's method. It provides an example of finding the roots of the quadratic function f(x) = x^2 - 6x + 8. The roots are found to be x1 = 4 and x2 = 2 using all three methods.

1. METODOS PARA HALLAR RAICES
(FUNCION CUADRATICA)

2. ..METODO DE FACTORIZACION..
F(X) = 푿ퟐ - 6X + 8
0 = 푋2 - 6X + 8 I) 푋1 - 4 = 0 푿ퟏ = ퟒ
푋2 - 6X + 8 = 0 II) 푋2 - 2 = 0 푿ퟐ = 2
(X – 4) (X – 2) = 0

3. ..METODO DE FORMULA GENERAL..
F(X) = 푿ퟐ - 6X + 8
a = 1 푥 =
−푏± 푏2−4푎푐
2푎
b = -6 푥 =
− −6 ± (−6)2−4(1)(8)
2(1)
c = 8 푥 =
6 ± 36−32
2

4. 푥 =
6 ± 4
2
푥 =
6 ± 2
2
푋1 =
6+2
2
푋2 =
6−2
2
푿ퟏ = 4 푿ퟐ = 2

5. ..METODO DE DIVISION SINTETICA O DE
RUFFINI..
F(X) = 푿ퟐ - 6X + 8
퐷8 = (±1, ±2, ±4, ±8)
X = 4 푿ퟏ = 4
X – 2 = 0 푿ퟐ = 2
X = 2