Question

What are the rational zeros of a polynomial function?

Answer 1

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`.