# Help Finding Roots of Polynomial

1. Jan 30, 2012

### theintarnets

1. The problem statement, all variables and given/known data
First find all rational zeros of f, then use the depressed equation to find all roots of the equation f(x) = 0.
f(x) = x^3 + 5x^2 - 8x + 2

2. Relevant equations

3. The attempt at a solution
Possible rational zeros: 2, -2, 1, -1
Synthetic division:

1 | 1 5 -8 2
_____1 6 -2
=============
1 6 -2 0

Quotient: x^2 + 6x - 2
Factored: (x + 3)^2 - 11

I would think that the answer would just be x = -3 ± √(11) but the answer in the book says: {1, -3 ± √(11)}
Where'd the 1 come from?

2. Jan 30, 2012

### rock.freak667

Remember, you divided by (x-1), so your equation become (x-1)(x^2+6x-2)=0 -> x= 1 in addition to the other roots you found.

3. Jan 30, 2012

### theintarnets

Ohhhhhhh! I see now, thank you!

4. Jan 31, 2012

### genericusrnme

synthetic division, oh lord
if you want a nicer division algorithm try this

or proper polynomial long division
... I really hated synthetic division :p

Last edited by a moderator: Sep 25, 2014
5. Jan 31, 2012

### eumyang

I believe we've had this discussion before, but there's nothing wrong with synthetic division. It's quick and pretty straightforward, IMO. Of course, if you're trying to divide a polynomial by a quadratic or a higher degree polynomial, then long division is the way to go.