Real and Imaginary Roots of Polynomials

Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial equation has at least one complex root.

Front

How many roots does a polynomial of degree n have?

Back

A polynomial of degree n has exactly n roots, counting multiplicities, in the complex number system.

Front

What is a real root?

Back

A real root is a solution to a polynomial equation that is a real number.

Front

What is an imaginary root?

Back

An imaginary root is a solution to a polynomial equation that is not a real number, typically expressed in the form a + bi, where i is the imaginary unit.

Front

What is the Conjugate Root Theorem?

Back

If a polynomial has real coefficients and a complex root a + bi, then its conjugate a - bi is also a root.

Front

Find the zeros of the polynomial: f(x) = (x-5)(2x+3)(7x-4)(x+6)

Back

x = 5, -3/2, 4/7, -6.

Front

What is the degree of the polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

True or False: The degree of the polynomial determines the number of roots.

Back

True.

Front

If a polynomial has a zero at x = 3, what does this imply?

Back

It implies that (x - 3) is a factor of the polynomial.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.