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

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

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