Question

Find all complex solutions of 3x^2+3x+4=0.

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

Answer 1

remember, √-1=i

also
for ax²+bx+c=0

`x=(-b+/-√(b^2-4ac))/(2a)`

so
given
3x²+3x+4=0
a=3
b=3
c=4


`x=(-3+/-√(3^2-4(3)(4)))/(2(3))`

`x=(-3+/-√(9-48))/(6)`

`x=(-3+/-√(-39))/(6)`

`x=(-3+/-(√(-1))(√(39)))/(6)`

`x=(-3+/-(i)(√(39)))/(6)`

`x=(-3+/-i√(39))/(6)`

the solutions (in a+bi form) are

`x=(-1)/(2)+(i√(39))/(6), (-1)/(2)-(i√(39))/(6)`