Example of ring with two maximal ideals such that the char of the quotients is $0$, respectively $p$.

Question

I am looking either for an example of a commutative ring with identity and two maximal ideals, such that the characteristic of one of the quotient rings is finite and the other characteristic is zero, or for an explanation why this is impossible.

Thanks in advance

Answer 1

How about $\mathbb{F}_p \oplus \mathbb{C}.$