Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra states that every non-constant polynomial equation of degree n has exactly n roots in the complex number system, counting multiplicities.

6

3

6

(x - 5)(x + 2)(x + 1)

A root of a polynomial is a value of x that makes the polynomial equal to zero.

The degree of a polynomial indicates the maximum number of roots it can have, including real and complex roots.

Complex roots are roots of a polynomial that have a real part and an imaginary part, typically expressed in the form a + bi.

If a polynomial has real coefficients, then any complex roots must occur in conjugate pairs (e.g., a + bi and a - bi).

The number of real roots can be determined using the polynomial's degree and the nature of its coefficients, often analyzed through the discriminant.