How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=10x^3-17x^2-7x+2#?

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Answer 1 · 2016-11-29T10:59:43

#-1/2, 1/5 and 2#

The number of changes in the signs of coefficients of f(x) is 2. So thr

limit for the number of positive roots is 2.

Likewise, this number for f(-x) is 1. So, the number of negative roots

is either 0 or 1.

As f(2) = 0, 2 is a zero of f, and so,

#(x-2)# is a factor of f. Easily, the other factor is

#10x^2+3x -1#. The zeros of this quadratic are # -1/2 and 1/5#.