1, formula method: the solution of a quadratic equation can be obtained by finding the root formula. According to the root formula, the solution of the quadratic equation in one variable is x = (-b √ (b 2-4ac))/(2a). By substituting the coefficients a, b and c in the equation, the values of the two roots are calculated.
2. Matching method: When the unary quadratic equation cannot be directly solved by the formula method, the matching method can be used. The basic idea of collocation method is to transform the equation into the difference between two squares by constructing a complete square form, so as to solve the equation. Specific steps can refer to related mathematics textbooks or online tutorials.
3. Factorization method: For a quadratic equation with one variable, if the factor can be decomposed into the product form of two linear factors, then the solution of the equation can be obtained by solving these two linear factors. Factorization method is suitable for simple equation coefficients.
4. Complete square formula: For the unary quadratic equation, if the form of the equation can be transformed by the complete square formula, then the solution of the equation can be obtained by solving the complete square formula. The formula of complete square is (a b) 2 = a 2 2ab+b 2, which can be solved by transforming the equation into the form of complete square.
One-variable quadratic equation:
The unary quadratic equation is an equation composed of quadratic term, linear term and constant term, and its general form is AX 2+BX+C = 0, where A, B and C are known coefficients, and A is not equal to 0. The value of the unknown quantity that makes the left and right sides of the unary quadratic equation equal is called the solution of the unary quadratic equation, also called the root of the unary quadratic equation.
Common application fields:
1, Physics: We can describe the trajectory of objects, projectile motion, free fall and other issues with a quadratic equation. For example, by solving a quadratic equation, we can calculate the throwing height, flight time, maximum height and other physical quantities.
2. Economics: The quadratic equation of one yuan can be applied to the problems of cost, income and profit in economics. For example, economic decision-making problems such as maximum profit output and minimum cost output can be determined by solving a quadratic equation.
3. Engineering: One-dimensional quadratic equation can be used to solve problems in engineering, such as structural design of buildings and circuit analysis. For example, the maximum bearing capacity of the bar, the current and voltage in the circuit can be determined by solving the quadratic equation of one variable.