Fundamental Theorem of Algebra

Front

What is the Fundamental Theorem of Algebra?

Back

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.

Front

What is the degree of a polynomial with 4 real roots and 2 complex roots?

Back

6

Front

What is the degree of a polynomial with roots -2, 4i, and -4i?

Back

3

Front

What is the total number of roots for the polynomial y = 4x^6 - 12x^5 - x^4 + 2x^3 - 6x^2 - 5x + 10?

Back

6

Front

If (x - 5) is a factor of f(x) = x^3 - 2x^2 - 13x - 10, what are the other factors?

Back

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

Front

What is a root of a polynomial?

Back

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

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

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

Front

What are complex roots?

Back

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

Front

What is the significance of complex conjugate roots in polynomials?

Back

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

Front

How do you determine the number of real roots of a polynomial?

Back

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