INDEX
Numbers and Sets
Complex Numbers
Exponentiation
Algebraic Transformations
Functions
Discrete Algebra
Basic Formulas
Graphics of Basic Functions
Algebraic Equations and Inequalities
Ship

Basic Conceptions

Properties of Equations and Inequalities

Graphical Interpretation of Solutions

Linear Equations and Inequalities

Linear Equations

Linear Inequalities

Linear Equations and Inequalities Involving Absolute Values

Linear Equations Involving Absolute Value

Linear Equations Involving a Few Absolute Values

Linear Inequalities Involving Absolute Value

Quadratic Equations and Inequalities

Quadratic Equations

Quadratic Equations and Quadratic Functions

Extreme Value of Quadratic Function

Quadratic Formula

Solving Quadratic Equations by Factoring

Quadratic Inequalities


Quadratic Equations
Key Topics Remaining:   Quadratic Equations and Quadratic Functions » Extreme Value of Quadratic Function » Quadratic Formula » Solving Quadratic Equations by Factoring » Quadratic Inequalities

The general form of a quadratic equation is

a x2 + b x + c = 0,

where  x  is the variable;  a,  b,  and  c  are constants .

Since the expression on the left-hand side is a polynomial of the second degree, the above equation is also called a second-degree equation.
It can also be rewritten in form of a monic quadratic equation, if to divide the both sides by the coefficient  a:

.

An equation of the form,

a x2 + c = 0,

is called an incomplete quadratic.
If  – c / a  > 0  then an incomplete quadratic has two solutions with opposite signs,

A quadratic equation of a common form can be solved by

  •    completing the perfect square;
  •    applying the quadratic formula;
  •    factoring.

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