Question

What is a rational zero?

Answer 1

A rational zero of a polynomial `f(x)` in a variable `x` is a fraction `p/q` such that `f(p/q) = 0` where `p` and `q` are integers.

Explanation:

A rational number is a number that can be expressed in the form `p/q` for some integers `p` and `q`.

A zero of an expression `f(x)` is a value of `x` such that `f(x) = 0`.

So a rational zero of an expression `f(x)` is basically a fraction `p/q` such that `f(p/q) = 0`.

For example, `2x^2-3x-5` has rational zeros `x=-1` and `x=5/2`, since substituting either of these values for `x` in the expression results in the value `0`.