Question

Rozłóż wielomian w(x) = 2x3-6x-4

na czynniki wiedząc ze liczba r= -1 jest jego pierwiastkiem.

Answer 1

w(x) = 2x^3 - 6x - 4

=================

w(-1)=0

=================

(2x^3 - 6x - 4) / (x + 1) = (2x^2 - 2x - 4)

"delta"=36

x1= -1

x2= 2

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

Pozdro :D

Answer 2

[2x³-6x-4]:[x+1]= 2x²-2x-4

-2x³-2x²

............

==== -2x²-6x-4

+2x² +2x

....................

====== -4x-4

+4x+4

.......................

================

 

2x³-6x-4=[x+1][2x²-2x-4]

Δ=b²-4ac=4+32=36

√Δ=6

x₁=[-b-√Δ]/2a=[2-6]/4=-1

x₂=[-b+√Δ]/2a=[2+6]/4=2

 

2x³-6x-4=[x+1][x+1][x-2]=[x+1]²[x-2]