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

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

Example
(a) Given x = 3 is the root of the quadratic equation $x^2+2x+p=0$ , find the value of p.
(b) The roots of the quadratic equation $3x^2+hx+k=0$   are -2 and 4. Find the value of h and k.

General Form of Quadratic Equation

General form of a quadratic equation is
$a{x}^2+bx+c=0$
where a, b, and c are constants and a≠0.

*Note that the highest power of an unknown of a quadratic equation is 2.

Example (Find the values of a, b and c)
Rewrite the following into the general form of a quadratic equation. Find the values of a, b, and c.
(a) ${(3x-5)}^2=0$
(b) (x - 8)(x + 8) = 0

Solution

What is a Quadratic Equation?

1. A quadratic equation is a polynomial equation of the second degree. 
2. A quadratic equation has only one variable 
3. The highest power of the variable is 2.

Example of Quadratic Equation
The followings are some examples of quadratic equations

• $2x^2+3x+4=0$
• $t^2=\frac{2}{5}$
• $y(6y-<!--\; -\; -->3)=5$
• $a-<!--\; -\; -->3y+2y^2=2$ where a is a constant.