Question

What are the possible rational zeros of `f(x) = 2x^3+5x^2-8x-10` ?

Answer 1

The possible rational zeros are:

`+-1/2, +-1, +-2, +-5/2, +-5, +-10`

Explanation:

Given:

`f(x) = 2x^3+5x^2-8x-10`

By the rational roots theorem, any rational zeros of `f(x)` are expressible in the form `p/q` for integers `p, q` with `p` a divisor of the constant term `-10` and `q` a divisor of the coefficient `2` of the leading term.

That means that the only possible rational zeros are:

`+-1/2, +-1, +-2, +-5/2, +-5, +-10`

In practice, none of these are zeros of `f(x)`, so it has no rational zeros.