Question
Sun September 09, 2012 By:

If two zeroes of the polynomial p(x) = x^4 - 6x^3 - 26x^2 + 138x - 35 are 2 + root 3 and 2 - root 3, find the other zeroes.

Expert Reply
Sun September 09, 2012
given that (x - 2 - root 3) and (x - 2 + root 3) are factors. this means x^2 - 4x + 1 is a factor of p(x).
now divide p(x) by the above polynomial which is its factor.
thereafter, find the zeroes of the obtained quotient.
the zeroes of the quotient will be the remaining two zeroes of p(x).
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