For example there's a curve $y=X^2-4X+7$ and a line $L: Y=mX-2$. Both never intersect at any given point. If we were to find the set of values of $m$ for which $L$ does not meet the curve, the solution will be as follows
Now here my teacher sets the inequality $b^2-4ac<0$.
My question is why when a curve and a line do not intersect each other then the above inequality is set to further solve it. Is $b^2-4ac<0$ when two lines don't meet?
Please also explain whether this inequality is set only when a curve and a line do not meet.