Mathematics: Find the solutions of the equation x4 − 2x3 − x2 + 2x = 0. (enter your answers as a comma-separated list.)

Find the solutions of the equation x4 − 2x3 − x2

Ответ:

georgesarkes12

15.01.2022

$S=\left \{ 0,-1,1,2 \right \}$

Step-by-step explanation:

There are several ways to solve this quartic equation. But since the coefficients, they repeat a=1,b=2,c=1,d=2, but e=0, and they are multiple of each other, then it is more convenient to work with factoring as the method of solving it.

As if it was a quadratic one.

$x^{4}-2x^{3}- x^{2} + 2x = 0\\x(x^{3}-2x^{2}-x+2)=0 \:Factoring \:out\\x[(x^{3}-2x^{2})+(-x+2)]=0 \:Grouping\\x[\mathbf{x^{2}}(x-2)+\mathbf{-1}(x+2)]=0 \:Rewriting\:the\:first\:factor\\x(x^{2}-1)(x-2)\:Expanding \:the \:first \:factor\\x(x-1)(x+1)(x-2)=0\\x=0,x=1,x=-1,x=2\\S=\left \{ 0,-1,1,2 \right \}$

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Ответ:

emmamanny

30.04.2023

Mathematics

x=6

Step-by-step explanation:

( x) +(x+2)=14

(2x+2)=14

(2x)=12

x=6

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Find the solutions of the equation x4 − 2x3 − x2 + 2x = 0. (enter your answers as a comma-separated list.)

Ответ:

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