Cubic equation with two unknown coefficients

  • Thread starter MegaDeth
  • Start date
  • #1
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Homework Statement



x^3 +px^2 + 56x + q = 0


I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given.

Homework Equations



Given that the three roots are all positive and are the first free terms of a geometric series with common ratio 2,

a. find the three roots of the equation.

b. find the values of p and q.


The Attempt at a Solution



I've work out the old roots,

roots one at a time = -p

roots two at a time = 56

product = -q
 

Answers and Replies

  • #2
tiny-tim
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Hi MegaDeth! :smile:
Given that the three roots are all positive and are the first free terms of a geometric series with common ratio 2 …
(i assume you mean the first three terms? :wink:)

start by calling the smallest root "r" …

then you know what the other two roots are :wink:
 
  • #3
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Hi MegaDeth! :smile:


(i assume you mean the first three terms? :wink:)

start by calling the smallest root "r" …

then you know what the other two roots are :wink:
Oh god, that's embarrassing. I didn't notice that mistake.

Ok, so the roots would be: r, r+2 and r+4? If so, how would I use these to find p and q?
 
  • #4
tiny-tim
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Ok, so the roots would be: r, r+2 and r+4? If so, how would I use these to find p and q?
r, 2r, 4r :wink:

try it, then ask :smile:
 
  • #5
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Sorry but I'm not familiar with this method. I don't know how to do it. :(
 
  • #6
tiny-tim
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well, write out the equations …

what are they?​
 
  • #7
SammyS
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Sorry but I'm not familiar with this method. I don't know how to do it. :(
What is the method that you're unfamiliar with ?
 

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