Fundamental Theorem of Algebra

[nycmathguy]

Section 2.5

The Fundamental Theorem of Algebra

If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system.

Is there an easier way to say the above statement?

 

[MathLover1]

Fundamental theorem of algebra, Theorem of equations proved by Carl Friedrich Gauss in 1799.

any polynomial of degree n has n roots but we may need to use complex numbers

 

[nycmathguy]

Fundamental theorem of algebra, Theorem of equations proved by Carl Friedrich Gauss in 1799.

any polynomial of degree n has n roots but we may need to use complex numbers

Any polynomial of degree n, where n > 0. Why must n be greater than zero?

 

[MathLover1]

Why must n be greater than zero?

because it is degree, if n=0 than x^n=x^0=1 which is monomial (just one integer)

 

[nycmathguy]

Why must n be greater than zero?

because it is degree, if n=0 than x^n=x^0=1 which is monomial (just one integer)

I get it. Makes sense.

Note: The sections are getting more intense. I will post less questions seeking a more elaborate reply from you per thread when time allows.