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Help Finding Roots of Polynomial 
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#1
Jan3012, 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? 


#2
Jan3012, 04:36 PM

HW Helper
P: 6,202

Remember, you divided by (x1), so your equation become (x1)(x^2+6x2)=0 > x= 1 in addition to the other roots you found.



#3
Jan3012, 04:37 PM

P: 64

Ohhhhhhh! I see now, thank you!



#4
Jan3112, 12:33 AM

P: 615

Help Finding Roots of Polynomial
synthetic division, oh lord
if you want a nicer division algorithm try this http://www.youtube.com/watch?v=VQ6jBYn3Oc or proper polynomial long division ... I really hated synthetic division :p 


#5
Jan3112, 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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