A second degree polynomial equation is called a quadratic equation.

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.

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.

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.

$ax^2+bx+c=0$

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

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.