To give definition to an equation root, it is necessary to deal with a concept of equation per se. It is intuitively simple to guess that the equation is an equality of two sizes. Understand value of an unknown component as a root of the equation. To find value of this unknown, the equation needs to be solved.
As a part of the equation there have to be two algebraic expressions equal among themselves. Each of these expressions contains unknown. Unknown of algebraic expressions also call variables. It is connected with the fact that each unknown can have one, two or unlimited number of values. For example, in the equation 5X-14=6 value at the unknown H only one: X =4.
For comparison we will take the equation of U-H=5. Here roots the infinite number can be found. The value of the unknown At will change depending on what is accepted value X and vice versa.
To define all possible values of variables – means to find equation roots. For this purpose the equation needs to be solved. It is carried out by means of mathematical operations as a result of which algebraic expressions, and together with them and the equation, are reduced to a minimum. As a result or the value of one unknown is defined, or the interdependence of two variables is established. To check fidelity of the decision it is necessary to substitute the found roots in the equation and to solve the turned-out mathematical example. As a result equality of two identical numbers has to turn out. If equality of two numbers did not turn out, then the equation is solved incorrectly and, respectively, roots are not found. For an example we will take the equation from one unknown: 2X-4=8+X. We find a root of this equation: 2X-X=8+4X=12C the found root we solve the equation and we receive: 2*12-4=8+1224-4=2020=20Уравнение it is solved truly. However if to take number 6 for a root of this equation, then the following will turn out: 2*6-4=8+612-4=148=14Уравнение it is solved incorrectly. Conclusion: number 6 is not a root of this equation. However not always roots can be found. The equations which do not have roots are called unsolvable. So, for example, the equation of X2=-9 as any value of the unknown H squared has to give positive number will have no roots. Thus, the root of the equation is a value of the unknown which is defined by a solution of this equation.