Roots of Quadratic Equations

Posted on April 18, 2020 by user

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

$x^{2} - 5 x + 6 = 0$ .

Answer:
When x = 1,

$\begin{array}{l} x^{2} - 5 x + 6 = 0 \\ (1)^{2} - 5 (1) + 6 = 0 \\ 2 = 0 \end{array}$
x = 1 does not satisfy the equation

When x = 2,

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

When x = 3

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

Conclusion:

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