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Please explain all rational roots of this equation!?!  Name all possible rational...

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babyryan95 | Honors

Posted July 18, 2012 at 5:37 PM via web

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Please explain all rational roots of this equation!?!

 

Name all possible rational roots of:

3x^4 - 5x^3 + 6x^2 + 2x + 4

It is assumed that all possibilities are both positive and negative. Ener positive values only. Enter as fractions from least to greatest, separated by a comma.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 18, 2012 at 6:10 PM (Answer #1)

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The possible rational roots of a polynomial with integer coefficients written in standard form (terms written in order of descending degree) are of the form `p/q` , where p is a divisor of the constant term, and q is a divisor of the leading coefficient.

The constant term is 4 so `p=+-1,+-2,+-4`

The leading coefficient is 3 so `q=+-1,+-3`

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The possible rational roots, ignoring negatives, and written in ascending order are:

`1/3,2/3,1,4/3,2,4`

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