Assignment 7.5 Roots and Zeros of Polynomials

Front

All zeros containing a square root sign come in pairs.

Back

True

Front

All imaginary roots come in pairs.

Back

True

Front

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

Back

3-5i

Front

Write a polynomial function of least degree with integral coefficients that has the given zeros: 5, -2i.

Back

x^3 - 5x^2 + 4x - 20

Front

Solve by using Rational Root Theorem: 2x^3 - 11x^2 + 12x + 9 = 0

Back

-1/2, 3, 3

Front

What is the Complex Conjugate Root Theorem?

Back

If a polynomial has real coefficients, then any complex roots must occur in conjugate pairs.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants.

Front

What is a zero of a polynomial?

Back

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

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution of a polynomial equation is a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you find the degree of a polynomial?

Back

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