The solution of a quadratic equation, or the value/s obtained after solving a quadratic

equation are known as the roots of the quadratic equation. The roots of a quadratic

equation are known by the following names as well:

if and only if

substituting the number in place of 'x' in the quadratic equation, the result is

true.

Thus we get 0 = 0 after simplifying the equation. This ensures that 5 is a root of the given quadratic equation.

In general, there are exactly two roots of a quadratic equation. To know why it is so, please go here:

equation are known as the roots of the quadratic equation. The roots of a quadratic

equation are known by the following names as well:

- Solutions of the quadratic equation
- Zeros of the quadratic equation
- x intercepts of the quadratic equation's graph

Mathematical definition:

Any real number 'alpha' is called a root/solution of a quadratic equation 'ax^{2}+ bx + c = 0'if and only if

a(alpha)

In simple words, a number is called the root of a quadratic equation only if on^{2}+ b(alpha) + c = 0 is truesubstituting the number in place of 'x' in the quadratic equation, the result is

true.

Example of a root of a quadratic equation:

For example, the, 5 is the root of the following quadratic equation because on putting x = 5 in it, we get LHS = RHS after simplification. That is,
Equation: x

Putting x = 5 in the above equation:^{2}- 2x - 15 = 0Put 5 in place of x in the equation: | 5^{2} - 2 * 5 - 10 |

Simplify the LHS: | 25 - 10 - 15 = 0 |

0 = 0 |

In general, there are exactly two roots of a quadratic equation. To know why it is so, please go here:

More examples :

- 4 and 3 are the roots of x
^{2}- 7x + 12 = 0 - 5 and 4 are the roots of x
^{2}- 9x + 20 = 0 - 2 and -1 are the roots of x
^{2}- x - 2 = 0

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