Quadratic irrational
Overview
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a quadratic irrational (also known as
a quadratic irrationality or quadratic surd) is an irrational number
Irrational number
In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number....
that is the solution to some quadratic equation
Quadratic equation
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
with rational coefficients. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their common denominator, a quadratic irrational is an irrational root of some quadratic equation whose coefficients are integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s.
