Answer
The equation has two complex solutions that are not real and are conjugates of each other.
Work Step by Step
The equation has $a=3, b=-1, \text{ and }c=4$.
To determine the character of the solutions of this equation, we need to find the value of the discriminant of the equation, which is $b^2 - 4ac$.
Substitute the values into this expression:
$b^2 - 4ac = (-3)^2 - 4(3)(4)$
$b^2 - 4ac = 9 - 4(3)(4)$
$b^2 - 4ac = 9 - 48$
$b^2 - 4ac = -39$
Since $-39 < 0$, the equation has two complex solutions that are not real and are conjugates of each other.
