Hi just had this plonked on me and feel it would make better sense if someone could explain it to me

Symmetric properties of the roots of polynomial equations

Cubics

Original Equation:

Ax³ + Bx² + Cx + D = 0

Sum of roots : α + β + γ = -B/A

'Roots in pairs' : βγ + γα + αβ = C/A

Product of the roots : αβγ = -D/A

New equation : x³ - (sum)x² + (pairs)x - (product) = 0

I could memorise all this but would rather know what it means and how it works.

Thanks =)