What are the possible integral zeros of #P(p)=p^4-2p^3-8p^2+3p-4#?

1 Answer
George C.
Jan 14, 2017

The "possible" integral zeros are: #+-1, +-2, +-4#

Actually #P(p)# has no rational zeros.

Explanation:

Given:

#P(p) = p^4-2p^3-8p^2+3p-4#

By the rational roots theorem, any rational zeros of #P(p)# are expressible in the form #p/q# for integers #p, q# with #p# a divisor of the constant term #-4# and #q# a divisor of the coefficient #1# of the leading term.

That means that the only possible rational zeros (which also happen to be integers) are:

#+-1, +-2, +-4#

In practice we find that none of these are actually zeros, so #P(p)# has no rational zeros.

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