If f(x) = ax^6 + bx^4 + cx^3 where a, b, and c are integers, how many distinct rational zeros could f(x) have

You can rewrite your function as

This implies that

Now, we have , so it counts as a solution.

On the other hand, depending on the coefficient a, b and c, the cubic equation

can have either one or three solutions.

So, we have the solution x=0, and then one or three solutions coming from the cubic part. The equation as a whole thus have either two or four solutions, depending on the coefficients.

answer is x<

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step-by-step explanation:

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