Answer:
see explanation
Step-by-step explanation:
Given
2x³ - x² + 18x - 9 = 0 ( factor the first/second and third/fourth terms )
x²(2x - 1) + 9(2x - 1) = 0 ← factor out (2x - 1) from each term
(2x - 1)(x² + 9) = 0
Equate each factor to zero and solve for x
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]
x² + 9 = 0 ⇒ x² = - 9 ⇒ x = ± 3i
The equation has 1 real solution and 2 complex solutions
x = [tex]\frac{1}{2}[/tex] ← real solution
x = ± 3i ← complex solutions
