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The rational zeros (or rational roots) of a function y = f(x) are the rational values of x for which y is zero. In graphical terms, these are the values at which the graph of y against x crosses (or touches) the x-axis - PROVIDED that the x value for these points are rational.

In the simplest cases, you can solve f(x) = 0 algebraically to find the rational zeros.

In other cases, you might need to solve f(x) = 0 by graphical methods, by trial and improvement or by numerical methods such as Newton-Raphson.

In all these cases, you need to confirm that the x value is rational.

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