When does a function: $f(x)=3ax^2 + 2bx + c $ has no solution?

Question

When does a function: $f(x)=3ax^2 + 2bx + c $ has no solution?

can i say that if the discriminant $4b^2 - 12ac$ is a negative number because according to the quadratic root formula square root portion is a negative number and square root of a negative number is undefined

Answer 1

Your approach is correct. When $4b^2-12 ac<0$, function $f$ has two complex roots (nonzero imaginary part). When $4b^2-12 ac \ge 0$ it has one or two distinct real roots.