Question

1). Descompuneti in factori:

a). x^2 - x - 2
b). x^2 + x - 6

Cu rezolvare vă rog!

Answer 1

Salut,

a) x²-x-2 = 0.

a = 1
b = -1
c = -2

∆ = b²-4ac
∆ = 1-4×(-2)
∆ = 1+8
∆ = 9.

x1 = (-b-√∆)/2a
x1 = (1-3)/2
x1 = -2/2
x1 = -1.

x2 = (-b+√∆)/2a
x2 = (1+3)/2
x2 = 4/2
x2 = 2.

a(x-x1)(x-x2) = (x+1)(x-2).


sau :

x²-x-2 = x(x-1)-2 = (x-1)(x-2).

b) x²+x-6 = 0.

a = 1
b = 1
c = -6

∆ = b²-4ac
∆ = 1-4×(-6)
∆ = 1+24
∆ = 25.

x1 = (-b-√∆)/2a
x1 = (-1-5)/2
x1 = -6/2
x1 = -3.

x2 = (-b+√∆)2/a
x2 = (-1+5)/2
x2 = 4/2
x2 = 2.

a(x-x1)(x-x2) = (x+3)(x-2).


Succes! :3

Answer 2

mai  de (vacanta de ) a 7-a asa fara aflarea lui x1 si x2, cu 'spargerea" convenabila a termenuluidin mijloc

x²+x-2=x²+2x-x-2=x(x+2)-(x+2)=(x+2)(x-1)


x²+x-6=x²+3x-2x-6=x(x+3)-2(x+3)=(x+3)(x-2)

as simple as that!