Answer:
x =
, x = ± i
Step-by-step explanation:
Given
5x³ - 2x² + 5x - 2 = 0 ( factor the first/second and third/fourth terms )
x²(5x - 2) + 1(5x - 2) = 0 ← factor out (x - 2) from each term
(5x - 2)(x² + 1) = 0
Equate each factor to zero and solve for x
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = 
x² + 1 = 0 ⇒ x² = - 1 ⇒ x = ±
= ± i
The polynomial is of degree 3 and has 3 roots, 1 real and 2 complex, that is
x =
← real root
x = ± i ← complex roots