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

1 Answer
Jul 15, 2017

Answer:

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.