Question

Find all complex solutions of 5x^2-6x+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
5x^2-6x+2=0
a=5
b=-6
c=2


`x=(-(-6)+/-√((-6)^2-4(5)(2)))/(2(5))`

`x=(6+/-√(36-40))/(10)`

`x=(6+/-√(-4))/(10)`

`x=(6+/-2i)/(10)`


`x=(3)/(5)+(i)/(5), (3)/(5)-(i)/(5)`