Thread: Algebraic Numbers

A number r is algebraic if there is a nonzero polynomial p(x) with integer coefficients such that r is a root of p(x) = 0.

Prove that every rational number is an algebraic number.

Originally Posted by thamathkid1729

A number r is algebraic if there is a nonzero polynomial p(x) with integer coefficients such that r is a root of p(x) = 0.

Prove that every rational number is an algebraic number.

Let q be any rational number. q=a/b, where a and b are integers.

bq-a=0

bx-a is the nonzero polynomial p(x) with integer coefficients such that q is a root of p(x)=0.

So, every rational number is an algebraic number.