Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$

Question

Prove that: $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$

We just learned about the characteristic/minimal polynomial and diagonalization but I am not sure if it has something to do with this question.

I'd be glad for guidance!

Answer 1

Consider the polynomial $X^2-aX+b \in \mathbb{C}[X]$. It has two roots ...