What are the rational zeros of a polynomial function?

1 Answer
May 30, 2016

Answer:

See explanation...

Explanation:

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

So some examples of typical polynomials might be:

#x^2+3x-4#

#3x^3-5/2x^2+7#

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

#f(x) = x^2+3x-4#

#g(x) = 3x^3-5/2x^2+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) = x^2+3x-4#.

A rational zero is a zero that is also a rational number, that is, it is expressible in the form #p/q# for some integers #p, q# with #q != 0#.

For example:

#h(x) = 2x^2+x-1#

has two rational zeros, #x=1/2# and #x=-1#

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