1.NounA complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers."The golden ratio (φ) is an algebraic number since it is a solution of the quadratic equation
x
2
−
x
−
1
=
0
{\displaystyle x^{2}-x-1=0}
, whose coefficients are integers.; The square root of a rational number,
m
n
{\displaystyle \textstyle {\sqrt {\frac {m}{n}}}}
, is an algebraic number since it is a solution of the quadratic equation
n
x
2
−
m
=
0
{\displaystyle nx^{2}-m=0}
, whose coefficients are integers."