Answer
both roots are imaginary.
Work Step by Step
For the equation $3x^2-x+4=0$, we have
$$a= 3, \quad b=-1, \quad c=4,$$ We check the value of the discriminant, as follows $$b^2 -4ac=1-4(3)(4)=1-48=-47$$ Since $-47$ is negative, then both roots are imaginary.
