When x takes any value in a certain interval or set u, the algebraic expression f(x) about x always satisfies the condition that it is greater than or equal to 0. We call it "always satisfactory" constant.
In other words, no matter what value the independent variable takes, the inequality relationship is established, but here we must distinguish the stem. If it is not clearly stated whether it is a quadratic inequality, we should pay attention to the situation that the coefficient of the quadratic term may be equal to 0.
Matters needing attention in calculating constancy
First of all, the inequality problem can be transformed into a comparison between a single constant and another constant with no independent variables. The other is to find the maximum value of a function.
If the function is greater than 0, the minimum value must be greater than 0 in a certain interval; On the other hand, if the function is less than 0, the maximum value should be less than 0 in a certain interval. Therefore, we must practice the problem of interval maximum of quadratic function in one variable and learn to apply it to the establishment of constants of this inequality.