1, when -=b3-4ac≥0, the quadratic trinomial, ax2+bx+c has two real roots, then ax2+bx+c can always be decomposed into the form of a(x-x 1)(x-x2). In this way, solving quadratic inequality can be reduced to solving two linear inequalities. The solution set of unary quadratic inequality is the intersection of the solution sets of these two unary linear inequality groups.

2. Solve quadratic inequality by collocation method.

3. Through the image of a quadratic function, the two intersections of the quadratic function image and the X axis, and then deduce the answer according to the required 0 ".

4. Passing through the roots on the number axis: When solving higher-order inequalities with the root axis method, the inequality is first turned into zero, then the factors at the other end are decomposed, and their zeros are found. These zeros are marked on the number axis, and then a smooth curve passes through these zeros in turn from the right upper end of the X axis.

The solution of this inequality greater than zero corresponds to the set of values of the real number x in the upper half of the x axis of this curve, and less than zero is the opposite. This method is called sequential axis marking root method.

The basic solution is to find two roots by using the formula method of quadratic equation in one variable, and then determine the interval of inequality solution set according to the inequality situation. To find the solution set of a univariate quadratic inequality is actually to move all the terms of this univariate quadratic inequality to the left of the inequality and discuss factorization and classification to solve the set.

Solving the unary quadratic inequality can transform the unary quadratic equation inequality into the form of quadratic function, find out the intersection of the function and the X axis, connect the unary quadratic inequality, quadratic function and unary quadratic equation, and solve the problem by mirror method, which simplifies the problem.

Data expansion:

The formula that uses the symbol ">" "< to represent the relationship between size is called inequality. An inequality represented by "≦" is also an inequality. Usually the number in inequality is a real number, and letters also represent real numbers.

The general form of inequality is F(x, y, ..., z)≤G(x, y, ..., z? )。 The common domain of analytic expressions on both sides is called inequality domain, which can represent both a proposition and a problem.