2.3 Solving Quadratic Equations

Solving Quadratic Equations

To solve a quadratic equation means to find all the roots of the quadratic equations.

Example:
Find the roots of the quadratic equations
a. $x^2=9$
b. $2x^2-<!--\; -\; -->98=0$

Answer:
 (a)
$\begin{array}{l}{x}^2=9\\ x=\pm <!--\; \pm \; -->\sqrt{9}\\ x=\pm <!--\; \pm \; -->3\end{array}$

(b)
$\begin{array}{l}2x^2-<!--\; -\; -->98=0\\ 2x^2=98\\ x^2=\frac{98}{2}=49\\ x=\pm <!--\; \pm \; -->\sqrt{49}=\pm <!--\; \pm \; -->7\end{array}$

A quadratic equation may be solve by using one of the following method

1. Factorisation
2. Completing the square
3. Using quadratic formula