Question

How to get x when x^3-x^2+x-1=0?

Answer 1

x = 1 or x = ± i

Explanation:

Note the sum of the coefficients

1 - 1 + 1 - 1 = 0

This indicates that x = 1 is a root, thus (x - 1) is a factor

Using long division or synthetic division, then

x³ - x² + x - 1 = (x - 1)(x² + 1), thus

(x - 1)(x² + 1) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x² + 1 = 0 ⇒ x² = - 1 ⇒ x = ±
`√(-1)` = ± i