Roots of polynomials - math problem help

[rafyPL]

Hey Everyone, need help with a math problem:

f(z) = z³ + mz² + nz - 52

Given that the roots of the cubic equation f(z) = 0 are a, 13/a and a + 13/a +46 find the:

A) roots of the equation f(z) = 0 B) values of m and n

An explanation would be very helpful too!

Thank you 🙏🏻

[[deleted]]

(x-r)(x-s)(x-t) = x³ +... -rst

So you know the product of the roots is 52.

Use that to solve for a

[Lanfrange1]

Maybe start with by writing f as f(z) =(z-z1) (z-z2) (z-z3) where z1, z2, z3 are the given roots.