**How to find the roots of an quadratic equation - Free Math Help**

# What is the root of the equation

The equation must contain two algebraic expressions that are equal to each other. Each of these expressions contains unknowns. Unknown algebraic expressions are also called variables. This is due to the fact that each unknown may have one, two or an unlimited number of values.

For example, in equation 5Х-14 = 6, the value of the unknown X is only one: X = 4.

For comparison, take the equation Y-X = 5. Here an infinite number can be found. The value of the unknown Y will vary depending on which value of X is accepted, and vice versa.

To determine all possible values of variables is to find the roots of the equation. For this, the equation must be solved. This is done through mathematical operations, as a result of which the algebraic expressions, and with them the equation itself, are reduced to a minimum. As a result, either the value of one unknown is determined, or the mutual dependence of two variables is established.

To check the accuracy of the solution, it is necessary to substitute the found roots into the equation and solve the resulting mathematical example. The result should be the equality of two identical numbers. If the equality of two numbers did not work out, then the equation is solved incorrectly and, accordingly, no roots were found.

For example, take the equation with one unknown: 2X-4 = 8 + X.

Find the root of this equation:

2X-X = 8 + 4

X = 12

With the found root, we solve the equation and get:

2*12-4=8+12

24-4=20

20=20

The equation is solved correctly.

However, if we take the number 6 as the root of this equation, we get the following:

2*6-4=8+6

12-4=14

8=14

The equation is solved incorrectly. Conclusion: the number 6 is not the root of this equation.

However, not always roots can be found. Equations that do not have roots are called insoluble. So, for example, there will be no roots for the equation X2 = -9, since any value of the unknown X, squared, should give a positive number.

Thus, the root of the equation is the value of the unknown, which is determined by solving this equation.

For example, in equation 5Х-14 = 6, the value of the unknown X is only one: X = 4.

For comparison, take the equation Y-X = 5. Here an infinite number can be found. The value of the unknown Y will vary depending on which value of X is accepted, and vice versa.

To determine all possible values of variables is to find the roots of the equation. For this, the equation must be solved. This is done through mathematical operations, as a result of which the algebraic expressions, and with them the equation itself, are reduced to a minimum. As a result, either the value of one unknown is determined, or the mutual dependence of two variables is established.

To check the accuracy of the solution, it is necessary to substitute the found roots into the equation and solve the resulting mathematical example. The result should be the equality of two identical numbers. If the equality of two numbers did not work out, then the equation is solved incorrectly and, accordingly, no roots were found.

For example, take the equation with one unknown: 2X-4 = 8 + X.

Find the root of this equation:

2X-X = 8 + 4

X = 12

With the found root, we solve the equation and get:

2*12-4=8+12

24-4=20

20=20

The equation is solved correctly.

However, if we take the number 6 as the root of this equation, we get the following:

2*6-4=8+6

12-4=14

8=14

The equation is solved incorrectly. Conclusion: the number 6 is not the root of this equation.

However, not always roots can be found. Equations that do not have roots are called insoluble. So, for example, there will be no roots for the equation X2 = -9, since any value of the unknown X, squared, should give a positive number.

Thus, the root of the equation is the value of the unknown, which is determined by solving this equation.

**Video: Quadratic Equations 05 - Nature and Location of Roots**

Roots of quadratic equation (SPM Add Maths)

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