Thread: geometric progression in cubic roots - small question

If a cubic equation has three real roots in geometric progression with common difference 2, then the roots are a, 2a and 4a (a indicating alpha)

Further to this, if the geometric progression had a common difference of 5, would this mean that the roots are either
a, 3a, 6a
or a, 3a, 9a?

I think it might be the first one but I'm not so sure - otherwise I wouldn't have to ask Does anyone know what it might be? Thanks

Originally Posted by db5vry

If a cubic equation has three real roots in geometric progression with common difference 2, then the roots are a, 2a and 4a (a indicating alpha)

Further to this, if the geometric progression had a common difference of 5, would this mean that the roots are either
a, 3a, 6a
or a, 3a, 9a?

I think it might be the first one but I'm not so sure - otherwise I wouldn't have to ask Does anyone know what it might be? Thanks

If the roots are in geometric progression then they have a common multiple, not a common difference. And if the common multiple is 5 then they will be a, 5a and 25a. If it is 3 then they will be a, 3a and 9a.