### Roots of Quadratic Equations

Roots of a quadratic equation are the values of variables/unknowns that satisfy the equation.**Example**:

Determine whether 1, 2, and 3 are the roots of the quadratic equation ${x}^{2}-5x+6=0$ .

**Answer**:

When x = 1,

$$\begin{array}{l}{x}^{2}-5x+6=0\\ (1{)}^{2}-5(1)+6=0\\ 2=0\end{array}$$

x = 1 does not satisfy the equation

When x = 2,

$$\begin{array}{l}{x}^{2}-5x+6=0\\ (2{)}^{2}-5(2)+6=0\\ 0=0\end{array}$$

x = 2 satisfies the equation.

When x = 3

$$\begin{array}{l}{x}^{2}-5x+6=0\\ (3{)}^{2}-5(3)+6=0\\ 0=0\end{array}$$

x = 3 satisfies the equation.

**Conclusion**:

- 2 and 3 satisfy the equation
${x}^{2}-5x+6=0$
, hence there are the
**roots**of the equation. - 1 does not satisfy the equation
${x}^{2}-5x+6=0$
, hence it is
**NOT**the root of the equation.