Quadratic Inequalities

We can have two inequalities. One where f(x)<0 and the other where f(x)>0.
Express y=f(x)=a*x^2 + b*x + c=0 as y=(x – m)*(x – n) and plot in number line.

The inequality, f(x) is less than zero when x lies between m and n and f(x) is greater than zero when x lies between (-∞,m) and (n, ∞). f(x) is zero at x = m and x = n.

Thus, the solution of:

f(x) =0: x = {m, n}.
f(x)<0:  x = ( m, n ).

f(x)<= 0: x = [m,n].
f(x)>0 : x = (-∞,m) and (n, ∞).

f(x)>=0 : (-∞,m] and [n, ∞).