I eas given this quesstion in one of my Linear Algebra course with the excercises regarding minimal polynomialsm eigenvalues and diagonalizable matrix:
Show that for any two numbers $a,b \in \mathbb{C}$ exist $c,d \in \mathbb{C}$ such that $c+d=a$ and $cd=b$.
I have no idea if and how it's related to the material we just covered, and have no clue how to attack it. I tried prooving it straight forward algebrically, but it's just got messy.
Any hints? clues? ideas?
Thanks :)
2026-03-28 20:49:53.1774730993
Complex numbers property proof.
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