What are the possible rational zeros of f(x)=2x3+5x2−8x−10 ?

1 Answer
George C.
Jul 15, 2017

The possible rational zeros are:

±12,±1,±2,±52,±5,±10

Explanation:

Given:

f(x)=2x3+5x2−8x−10

By the rational roots theorem, any rational zeros of f(x) are expressible in the form pq 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:

±12,±1,±2,±52,±5,±10

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

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