In elementary algebra, a quadratic equation is any equation having the form

$ax^2+bx + c = 0$

where $x$ represents an unknown, and $a,\ b,\ and\ c$ represent known numbers such that $a$ is not equal to $0$.

If $a = 0$, then the equation is linear, not quadratic.

The numbers $a,\ b,\ and\ c$ are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The degree of a quadratic equation is 2.

$21x^2-8x-4=0 \ where \ a=21, \ b=-8 \ and \ c=-4$

$6x^2+5x-6=0 \ where \ a=6, \ b=5 \ and \ c=-6$

Every quadratic equation $ax^2+bx + c = 0$ is satisfied by two values say $p \ and \ q$. These values, $p \ and \ q$, are said to be the root of the equation.

What this also means is that $ax^2+bx + c = (x - p)(x - q) = 0$

There are two ways to solve the quadratic equations.

1. Factorization Method
• Step 1: Factorize $ax^2+bx + c = (x - p)(x - q) = 0$
• Step 2: Equate each linear part to zero.
• Step 3: Hence $x = p \ and \ x = q$

Using the formula

• Step 1: From the quadratic equation, first identify $a,\ b,\ and\ c$.
• Then use the following formula

$x =$ $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$