Zeros occur when f(x) = 0. To find the zeros, the equation becomes
0 = 3x^2 + 2x + 4
We can factor, use the quadratic formula, or use the graphing calculator, but since the function isn't factorable we have to use the quadratic formula.
But the question asks for real zeros, which mean they have to cross the x-axis and f(x)=0. Since its not factorable then there are imaginary roots, which means when the function is graphed it will be floating above the x-axis (because of a positive coefficient of x^2) and not cross it.
In short. there are no real roots because the graph does cross or touch the x-axis
