1, concept definition: the root of the equation refers to the value of the unknown that can make the left and right sides of the equation equal. The solution of an equation is the value of an unknown quantity that can make the values on both sides of the equation equal. This is the most essential difference of root harmony.

2. Existence range: For a given equation, all roots can be solved, but not all solutions are roots of the equation. In other words, the solution may be the root of the equation or the pseudo solution of the equation. So when solving the equation, we need to check whether the solution is the root of the equation.

3. Solutions: For the roots of the equation, we usually need to find all the solutions that can make the equation hold. Therefore, when solving the roots of equations, we usually use graphic method, algebraic method or numerical calculation method. For the solution of the equation, we need to find the specific unknown value that can make the equation hold. Therefore, when solving the solutions of equations, we usually use algebraic methods or mathematical analysis methods.

Main applications of equation roots;

1, piecewise function: In mathematics, piecewise function is a very common function form. Piecewise functions usually have different analytical expressions in different intervals, and there are usually some common parts between these analytical expressions. The intersection of these common parts is the root of piecewise functions. Therefore, by solving the root of the equation, we can find the piecewise point of the piecewise function, and then get the analytical formula of the function.

2. Circuit analysis: In circuit analysis, the node voltage and branch current in the circuit are interrelated, and the relationship between them can be expressed by equations. The roots of the equation are the values of node voltage and branch current. By solving the root of the equation, the current and voltage of each branch in the circuit can be obtained, and then the properties and characteristics of the circuit can be analyzed.

3. Economic model: In the economic model, the roots of the equation can represent the equilibrium values of various economic variables. For example, in the supply-demand model, the root of the equation can represent the price and quantity when the market reaches equilibrium. By solving the root of the equation, we can predict the equilibrium state of the market, analyze the stability and changing trend of the market, and provide reference for the formulation of economic policies.