Question

What are the solutions of 2x^2-6x+5=0

Answer 1

Answer: x=3+i/2 or x=3-i/2

APEX

Answer 2

x =
`(3)/(2)` ±
`(1)/(2)`i

the equation has no real zeros but instead has 2 complex zeros

the discriminant = b² - 4ac

with a = 2, b= - 6, c = 5

b² - 4ac = (-6)² - (4 × 2 × 5 ) = -4

since b² - 4ac < 0 there are no real zeros

using the quadratic formula

x = ( 6 ± √(- 4 ) )/4 = ( 6 ± 2i ) / 4

x =
`(6)/(4)` ±
`(2)/(4)` i

=
`(3)/(2)` ±
`(1)/(2)` i