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$x^3- 3x + 2 = 0$

Using the Horner scheme, I can find easily the roots of the equation:

$x_1 = x_2 = 1 $ and $x_3 = 2.$

How can I find them using other method ?

neelkanth
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Florin M.
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  • What do you mean by "Horner scheme"? The rational root test here gives values to test to find any rational roots. The fact that the sum of coefficients is zero tells you that $1$ is a root. Taking the derivative will enable you to identify any multiple roots. Since this is a cubic, once you have one root, you are left with a quadratic, and you know how to solve that. – Mark Bennet Dec 06 '18 at 07:32

2 Answers2

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Notice that $x=1$ is a root from rational root test.

$$x^3-3x+2=(x-1)(x^2+x-2)=(x-1)(x-1)(x+2)=(x-1)^2(x+2)$$

Siong Thye Goh
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There are formulas to solve the ternary and quaternary equations. This is classical mathematics, done hundreds of years ago. Look up Cardano's formula and Ferrari's formula.

A. Pongrácz
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