Odpowiedzi

2010-03-08T23:49:41+01:00
A.) x³+3x²-9x-27=0
x³+3x²-9x-27=0 => x²(x+3)-9(x+3)=(x²-9)(x+3)(x-3)(x+3)(x+3)=(x-3)(x+3)² Odp x∈{-3;3}
b.) 3x³+x²-4x=0
3x³+x²-4x=0 => x(3x²+x-4)=0 =>
Δ=1+4×4×3=49 √Δ=7
x1=(-1-7)/6=-8/6=-4/3
x2=(-1+7)/6=6/6=1
Odp x∈{-4/3;0;1}
2.
x²+3x+1
________________
(x³+x²-5x-2):(x-2)
-x³+2x²
------------
3x²-5x-2
-3x²+6x
--------------
x-2
-x+2
-------------
0
W(x)= x³+x²-5x-2=(x²+3x+1)(x-2)
Δ=9-4×1×1=5 √Δ=√5
x1=(-3-√5)/2
x2=(-3+√5)/2
Odp x∈{(-3-√5)/2;(-3+√5)/2;2}