How do you find all the zeros of # f(x)=2x^3-13x^2+22x-8#?

1 Answer
Apr 1, 2016

Answer:

Use the Rational Factor Theorem to identify rational zeros.

Explanation:

According to the Rational Factor Theorem
if #2x^3-13x^2+22x-8# has rational zeros
they must be in the set
#color(white)("XXX")+-("factors of 8")/("factors of 2")=+-({1,2,4,8})/({1,2})#
Evaluating the equation for each possibility:

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identifies the zeros as #{color(red)(1/2),color(blue)(2),color(brown)(4)}#
which implies the factoring:
#color(white)("XXX")(color(red)(2x-1))(color(blue)(x-2))(color(brown)(x-4))#