[Verse 1]
In the realm where numbers dance with mystery's call
Every polynomial must find its home after all
Complex coefficients spinning through the night
At least one root awaits in C's infinite sight
[Chorus]
Every polynomial finds its zero
In the complex plane, our mathematical hero
N degree means N roots counting each repeat
The Fundamental Theorem makes the circle complete
No escape, no exception to this rule
C is algebraically closed, the ultimate tool
[Verse 2]
From quadratic struggles to cubic maze
We've extended numbers through confusing days
Real wasn't enough, we needed something more
Complex numbers opened up the final door
[Chorus]
Every polynomial finds its zero
In the complex plane, our mathematical hero
N degree means N roots counting each repeat
The Fundamental Theorem makes the circle complete
No escape, no exception to this rule
C is algebraically closed, the ultimate tool
[Bridge]
Multiplicity matters when we count each solution
Some roots hide behind their own resolution
But add them all up and the theorem stays true
Degree equals roots, this fact will see you through
[Verse 3]
No more crises demanding new extensions
Complex plane contains all our polynomial intentions
What began with solving simple equations ends
In C where every polynomial transcends
[Final Chorus]
Every polynomial finds its zero
In the complex plane, our mathematical hero
N degree means N roots counting each repeat
The Fundamental Theorem makes the circle complete
Algebraically closed, our number quest is done
In C every polynomial battle can be won
[Outro]
The theorem stands eternal, proven and complete
Where complex numbers and polynomials meet