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Cubic Roots 
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#1
Dec610, 11:56 AM

P: 53

1. The problem statement, all variables and given/known data
The equation: x^3 + ax + b = 0 has 3 roots, u, p and q. Give the general solution for for an equation with roots (u/p)+(p/u), (p/q)+(q/p) and (u/q)+(q/u) 2. Relevant equations u + p + q = 0 upq = b up + uq + pq = a If you can solve it you probably already knew those. 3. The attempt at a solution Well I've just done lots of fiddling with algebra and got a pretty nasty looking solution, and I'm not even sure if it's right. What I was trying to do was express one of the new roots in terms of a, b and u, and then plug back in to the original equation for the new equation. I've got a pretty rough looking solution but I wanted to see if anyone could find a elegant way of solving this or if it is just lots of scruffy algebra. Thanks. 


#2
Dec610, 12:08 PM

HW Helper
P: 6,202

You'll need to expand out
[x((u/p)+(p/u))][x((p/q)+(q/p))][x((u/q)+(q/u))]=0 and then use the conditions given in your relevant equations. I don't think there is a simpler way. EDIT: I think you can say in general you will have Ax^3+Bx^2+Cx+D=0 with the roots required, the sum will be B/A and then you can just simplify the sum of the roots and get B/A and so on. 


#3
Dec610, 12:09 PM

P: 53




#4
Dec610, 12:10 PM

HW Helper
P: 6,202

Cubic Roots



#5
Dec710, 01:48 PM

P: 53




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