Quadratic equation problems

Question

Find the range of values of h if $g(x)=3 x²+2 x+2 h$ is always positive.

Should I use $b²-4 a c>0$ to get the correct answer?

Answer 1

Hint:

since the coefficient of $x^2$ is $3>0$, the sign of $g(x)$ is always positive if $g(x)=0$ has no real roots.