Quadratic Equation

Quadratic is an expression or an equation that contains the variable squared, but not raised to any higher power. Quadratic equation in $x$ contains $x^2$ but not $x^3$.

The general quadratic equation is expressed as: \[ Ax^2 + Bx + C = 0 \] where $A$, $B$, and $C$ are real numbers and $A$ $\pm$ $0$.

When $B = 0$, quadratic equation is known as a pure quadratic equation.

A quadratic equation in $x$ is also known as a second-degree polynomial equation.

The solution to a quadratic equation is either by factoring or by the use of the quadratic formula: \[ x = \frac{-B \pm \sqrt{B^2 – 4AC}}{2A} \] The quantity $\sqrt{B^2 – 4AC}$ in the above equation is known as the discriminant. The discriminant will determine the nature of the roots of the quadratic equation.

The table below shows the value of the discriminant and its corresponding nature of roots.

$\sqrt{B^2 – 4AC}$	Nature of Roots
$0$	only one root (real and equal)
$>0$	real and unequal
$<0$	imaginary and unequal

The sum and product of the roots of a quadratic equation can be solved even without using factoring or quadratic formula as long as the general equation is given.