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- Homework Statement
- The cubic equation ##x^3-3x^2+4=0## has roots ##∝, β## and ##ϒ##. Find the cubic equation with roots ##2∝, 2β## and ##2ϒ##.

- Relevant Equations
- cubic equations with related roots

##\sum ∝=3##

##\sum ∝β=0##

##∝βγ=-4##

##\sum2 ∝=6##

##\sum 2∝.2β##=4##\sum ∝β=0##

##2∝.2β.2γ=-32##

we then end up with

##x^3-6x^2+0x+32=0##

##x^3-6x^2+32=0##

i am looking for alternative methods ...

##\sum ∝β=0##

##∝βγ=-4##

##\sum2 ∝=6##

##\sum 2∝.2β##=4##\sum ∝β=0##

##2∝.2β.2γ=-32##

we then end up with

##x^3-6x^2+0x+32=0##

##x^3-6x^2+32=0##

i am looking for alternative methods ...