Roots of Quadratic Equation

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