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.

### 1 Answer | Add Yours

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`

------------------------------------------------------------------

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

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

-----------------------------------------------------------------

**Sources:**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes