Question

3x ^ 3 - 3x ^ 2 - 6x = 0​

Answer 1

Odpowiedź:

3x³-3x²-6x=0

3x(x²-x-2)=0            Δ=b²-4ac=1+8=9           √Δ=3

x1=0                   x2=(-b-√Δ)/2a=( 1-3)/2=-1        

 x3=(-b+√Δ)/2a=(1+3)/2=2

Szczegółowe wyjaśnienie:

Answer 2

Odpowiedź:

[tex]\huge\boxed{x\in\{-1,0,2\}}[/tex]

Równanie wielomianowe

[tex]3x^{3}-3x^{2}-6x = 0\\\\3x(x^{2}-x-2) = 0\\\\3x = 0 \ \vee \ x^{2}-x-2 = 0\\\\1)\\3x = 0\\\\\underline{x_{o} = 0}\\\\Lub\\\\2)\\x^{2}-x-2 = 0\\\\a = 1, \ b = -1, \ c = -2\\\\\Delta = b^{2}-4ac = (-1)^{2}-4\cdot1\cdot(-2) = 1+8 = 9\\\\\sqrt{\Delta} = \sqrt{9} = 3\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} =\frac{-(-1)-3}{2\cdot1} =\frac{1-3}{2} =\frac{-2}{2} = -1[/tex]

[tex]x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-1)+3}{2\cdot1} = \frac{1+3}{2} = \frac{4}{2} = \underline{2}[/tex]

[tex]x = -1 \ \vee \ x=0 \ \vee \ x=2\\\\x \in \{-1,0,2\}[/tex]