Math Doubts

Quadratic equations

Introduction to Quadratic equations and learn how to solve quadratic equations in different methods.

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.

$ax^2+bx+c=0$



Follow us
Email subscription
Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more