Step 1: Understanding the Concept:
Eukaryotic cells contain multiple distinct types of nuclear RNA polymerase enzymes, each responsible for transcribing a specific class of genes.
Step 2: Detailed Explanation:
Let us review the roles of the different RNA polymerases found in eukaryotic cells:
1. RNA Polymerase I: Located in the nucleolus, this enzyme is responsible for synthesizing the major ribosomal RNA precursor ($45\text{S}$ rRNA), which is processed into the $28\text{S}$, $18\text{S}$, and $5.8\text{S}$ rRNA subunits.
2. RNA Polymerase II: Located in the nucleoplasm, this enzyme transcribes all protein-coding genes to synthesize messenger RNA (mRNA) precursors (pre-mRNA). It is also responsible for transcribing most microRNAs (miRNAs) and small nuclear RNAs (snRNAs).
Thus, RNA Polymerase II is the enzyme required for mRNA synthesis.
3. RNA Polymerase III: Also located in the nucleoplasm, this enzyme transcribes small, stable non-coding RNAs, including transfer RNA (tRNA), the $5\text{S}$ ribosomal RNA subunit, and the U6 snRNA.
4. Reverse Transcriptase: This is an enzyme found in retroviruses that synthesizes complementary DNA (cDNA) from an RNA template, rather than transcribing genomic DNA into mRNA.
Therefore, eukaryotic mRNA is synthesized by RNA Polymerase II.
Step 3: Final Answer:
The enzyme required for mRNA synthesis is RNA polymerase II, corresponding to option (D).