Math Doubts

Quadratic equation

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.

$ax^2+bx+c=0$

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved