Question

cuales son las soluciones de la siguiente ecuacion x4-x3-7x2+x+6=0​

Answer 1

Respuesta:

x^4-x^3-7x^2+x+6 = 0

x^4-x^3-7x^2+7x-6x+6 = 0

x^3(x-1)-7x^2+7x-6x+6 = 0

x^3(x-1)-7x(x-1)-6(x-1) = 0

(x-1)(x^3-7x-6) = 0

(x-1)(x^3-7x-6+x^2-x^2) = 0

(x-1)(x^3-x-6x+x^2-x^2) = 0

(x-1)(x^2(x+1)-x-6x-6 ) = 0

(x-1)(x^2(x+1)-x(x+1)-6x-6) = 0

(x-1)(x^2(x+1)-x(x+1)-6(x+1)) = 0

(x-1)((x+1)(x^2-x-6)) = 0

(x-1)((x+1)(x^2-3x+2x-6 )) = 0

(x-1)((x+1)(x(x-3)+2(x-3)) = 0

(x-1)((x+1)(x-3)(x+2)) = 0

(x-1)(x+1)(x-3)(x+2) = 0

x1 = 1 , x2 = -1 , x3 = 3 y x2 = -2

Explicación paso a paso: