Finding Real and Complex Roots of Polynomials

Front

What are 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 conjugate of 2 + √3?

Back

2 - √3

Front

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

Back

True

Front

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

Back

3

Front

What does the Fundamental Theorem of Algebra state about the total number of solutions of a polynomial?

Back

A polynomial of degree n has exactly n roots (counting multiplicities).

Front

Define a polynomial.

Back

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the degree of the polynomial 3x^4 - 5x^3 + 2?

Back

4

Front

How many complex roots does a polynomial of degree 5 have?

Back

5 (including real roots as complex roots with zero imaginary part).

Front

What is the relationship between the coefficients of a polynomial and its roots?

Back

The sum and product of the roots can be expressed in terms of the coefficients (Vieta's formulas).

Front

What is a complex root?

Back

A complex root is a solution to a polynomial equation that has a real part and an imaginary part.