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Help Finding Roots of Polynomial

by theintarnets
Tags: depressed equation, roots, zeros
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Jan30-12, 04:07 PM
P: 64
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?
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Jan30-12, 04:36 PM
HW Helper
P: 6,202
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.
Jan30-12, 04:37 PM
P: 64
Ohhhhhhh! I see now, thank you!

Jan31-12, 12:33 AM
P: 615
Help Finding Roots of Polynomial

synthetic division, oh lord
if you want a nicer division algorithm try this
or proper polynomial long division
... I really hated synthetic division :p
Jan31-12, 03:29 PM
HW Helper
P: 1,347
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.

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