What are the rational zeros of a polynomial function?

1 Answer
May 30, 2016

See explanation...

Explanation:

A polynomial in a variable x is a sum of finitely many terms, each of which takes the form akxk for some constant ak and non-negative integer k.

So some examples of typical polynomials might be:

x2+3x4

3x352x2+7

A polynomial function is a function wholse values are defined by a polynomial. For example:

f(x)=x2+3x4

g(x)=3x352x2+7

A zero of a polynomial f(x) is a value of x such that f(x)=0.

For example, x=4 is a zero of f(x)=x2+3x4.

A rational zero is a zero that is also a rational number, that is, it is expressible in the form pq for some integers p,q with q0.

For example:

h(x)=2x2+x1

has two rational zeros, x=12 and x=1

Note that any integer is a rational number since it can be expressed as a fraction with denominator 1.