Question

Find all complex solutions of 4x^2-5x+2=0.

(If there is more than one solution, separate them with commas.)

Answer 1

we use quadratic formula for that one
remember that √-1=i

so

for
ax^2+bx+c=0

`x=(-b+/-√(b^2-4ac))/(2a)`
so
given
4x^2-5x+2=0
a=4
b=-5
c=2


`x=(-(-5)+/-√((-5)^2-4(4)(2)))/(2(4))`

`x=(5+/-√(25-32))/(8)`

`x=(5+/-√(-7))/(8)`

`x=(5+/-i√(7))/(8)`

so in complex form (a+bi)

`x=(5)/(8)+(i√(7))/(8), (5)/(8)-(i√(7))/(8)`