Quadratic equations

A second degree polynomial equation is called a quadratic equation.

Introduction

An expression is a mathematical representation of one or more interconnected unlike terms and it is usually formed for representing a quantity mathematically. Sometimes, one of the terms in an expression can be a second degree term as its highest degree term. The meaning of quadratic is a power of $2$. Hence, an expression which consists a second degree term as highest degree term, is called a quadratic expression.

The quadratic expression is made to equal to zero to obtain roots of the variable. So, the equation is called a quadratic equation. A quadratic equation can be a monomial, binomial and even trinomial.

Examples

Observe the some of the quadratic expressions to have basic knowledge on it.

$(1) \,\,\,\,\,\,$ $6x^2$

$(2) \,\,\,\,\,\,$ $-7\sin^2{\theta}+9\sin{\theta}$

$(3) \,\,\,\,\,\,$ $5p^2+10$

$(4) \,\,\,\,\,\,$ $-4\dfrac{d^2m}{dt^2}+7\dfrac{dm}{dt}-3$

$(5) \,\,\,\,\,\,$ $10z^2-z-1$

All of them are quadratic expressions. If we made them equal to zero, then they are called quadratic equations.

$5p^2-19p+10 = 0$ is an example equation for a quadratic equation.

Algebraic form

The mathematical concept algebra is used to represent the quadratic equations in general form.

$a$, $b$ and $c$ are constants and $x$ is a variable. A quadratic equation is written generally in algebraic form as follows.

$ax^2+bx+c=0$