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# help

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One of the roots of x^3 - 5x^2 + 5x - 1 = 0 is 2 - sqrt(3).  What are the other two roots?

Dec 5, 2019

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One of the roots of x^3 - 5x^2 + 5x - 1 = 0 is 2 - sqrt(3).  What are the other two roots?

Hallo Guest

$$I\ assume: x_1 = 1$$

$$(x^3 - 5x^2 + 5x - 1):(x-1)=\color{blue}x^2-4x+1$$

$$\underline{x^3\ -\ x^2}$$

$${-4x^2+5x}$$

$$\underline{-4x^2+4x}$$

$$x-1$$

$$\underline{x-1}$$

$$0$$

$$x_1=1$$

$$x^2-4x+1=0\\ x=2\pm\sqrt{4-1}\\$$

$$x_2=2+\sqrt{3}\\ x_3=2-\sqrt{3}$$

!

Dec 5, 2019