Quadratic equation: Difference between revisions
No edit summary |
No edit summary |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
In [[Algebra (nonfiction)|algebra]], a '''quadratic equation''' (from the Latin ''quadratus'' for "square") is any equation having the form ax^2+bx+c=0 where ''x'' represents an unknown, and ''a'', ''b'', and ''c'' represent known numbers such that ''a'' is not equal to 0. | [[File:Quadratic_equation.jpg|thumb|A quadratic equation is any equation having the form ax^2+bx+c=0.]]In [[Algebra (nonfiction)|algebra]], a '''quadratic equation''' (from the Latin ''quadratus'' for "square") is any [[Equation (nonfiction)|equation]] having the form ax^2+bx+c=0 where ''x'' represents an unknown, and ''a'', ''b'', and ''c'' represent known [[Number (nonfiction)|numbers]] such that ''a'' is not equal to 0. | ||
If ''a'' = 0, then the equation is [[Linear equation (nonfiction)|linear]], not quadratic. | If ''a'' = 0, then the equation is [[Linear equation (nonfiction)|linear]], not quadratic. | ||
The numbers ''a'', ''b'', and ''c'' are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. | The numbers ''a'', ''b'', and ''c'' are the [[Coefficient (nonfiction)|coefficients]] of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. | ||
Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of ''x'' that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two. | Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of ''x'' that are non-negative integers, and therefore it is a [[Algebraic equation (nonfiction)|polynomial equation]], and in particular it is a second degree polynomial equation since the greatest power is two. | ||
Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorizing, by completing the square, by using the [[Quadratic formula (nonfiction)|quadratic formula]], or by graphing. | Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorizing, by completing the square, by using the [[Quadratic formula (nonfiction)|quadratic formula]], or by [[Graph of a function (nonfiction)|graphing]]. | ||
Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC. | Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC. | ||
| Line 14: | Line 14: | ||
<gallery> | <gallery> | ||
File:Quadratic_formula.svg|link=Quadratic formula (nonfiction)|The [[Quadratic formula (nonfiction)|Quadratic formula]], used to find the value of x in the quadratic equation. | |||
</gallery> | </gallery> | ||
| Line 24: | Line 25: | ||
* [[Algebra (nonfiction)]] | * [[Algebra (nonfiction)]] | ||
* [[Algebraic equation (nonfiction)]] | |||
* [[Coefficient (nonfiction)]] | |||
* [[Equation (nonfiction)]] | |||
* [[Graph of a function (nonfiction)]] | |||
* [[Linear equation (nonfiction)]] | * [[Linear equation (nonfiction)]] | ||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
* [[Number (nonfiction)]] | |||
* [[Quadratic formula (nonfiction)]] | * [[Quadratic formula (nonfiction)]] | ||
Latest revision as of 19:38, 1 December 2017
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form ax^2+bx+c=0 where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0.
If a = 0, then the equation is linear, not quadratic.
The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.
Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorizing, by completing the square, by using the quadratic formula, or by graphing.
Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC.
In the News
The Quadratic formula, used to find the value of x in the quadratic equation.
Fiction cross-reference
Nonfiction cross-reference
- Algebra (nonfiction)
- Algebraic equation (nonfiction)
- Coefficient (nonfiction)
- Equation (nonfiction)
- Graph of a function (nonfiction)
- Linear equation (nonfiction)
- Mathematics (nonfiction)
- Number (nonfiction)
- Quadratic formula (nonfiction)
External links:
- Quadratic equation @ Wikipedia