How is a quadratic inequality different from a quadratic equation?
one is an inequality, the other is not. :-)
An equation will have 0,1, or 2 roots.
for example,
(x-3)(x+4) = 0
is true when x=3 or x = -4.
(x-3)(x+4) < 0
is the interval from -4 to 3, where y < 0.
Just as the equation, the inequality may have an interval, or a point for a solution, or no solution at all.
x^2 <= 0 has only x=0 for a solution.
x^2 > 0 will have two intervals for a solution: (-oo,0) U (0,oo)
x^2 < 0 has no real solutions at all