Question

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

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

Answer 1

Given equation is
`3x^2 + 3x + 4 = 0`

Now we can compare it with general form of quadratic equation (
`ax^2 + bx + c = 0`)
a = 3 , b = 3 and c = 4

Now we can apply quadratic formula which is given as

`x =( -b+/- √(b^2-4ac) )/(2a)`

Now we can plugin value of a , b or c

`x = (-3+/- √((3)^2 - 4*3*4) )/(2*3)`

`= (-3+/- √(9 - 48) )/(6) = (-3+/- √(-39) )/(6)`
In general we know
`√(-1) = i`
So we can write
`√(-39 ) = √(-1) * √(39) = i √(39)`
So

`x = (-3+/-i √(39) )/(6)`
So
`x = (-3+i √(39) )/(6)` or
`x = (-3- √(39) )/(6)`