Cubic equation with two unknown coefficients

[MegaDeth]

Homework Statement

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

 

[tiny-tim]

Hi MegaDeth!

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? )

start by calling the smallest root "r" …

then you know what the other two roots are ​

 

[MegaDeth]

Hi MegaDeth!


(i assume you mean the first three terms? )

start by calling the smallest root "r" …

then you know what the other two roots are ​

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?

 

[tiny-tim]

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

try it, then ask ​

 

[MegaDeth]

Sorry but I'm not familiar with this method. I don't know how to do it. :(

 

[tiny-tim]

well, write out the equations …

what are they?​

 

[SammyS]

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 ?