Polynomials Given a Zero

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

Front

How many zeros does the polynomial f(x) = x^5 - 3x^3 + x have?

Back

5

Front

What does the Conjugate Root Theorem state?

Back

The Conjugate Root Theorem states that if a polynomial has real coefficients and a complex zero (a + bi), then its conjugate (a - bi) is also a zero.

Front

If one zero of a polynomial is 7 - 5i, what is the other zero?

Back

7 + 5i

Front

True or False: The solution, root, x-intercept, and zero of a polynomial are all the same thing.

Back

True

Front

What is an imaginary root?

Back

An imaginary root is a solution to a polynomial equation that cannot be expressed as a real number, typically involving the imaginary unit 'i', where i^2 = -1.

Front

True or False: All imaginary roots come in pairs.

Back

True

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

True or False: All zeros containing a square root sign come in pairs.

Back

True

Front

What is the degree of a polynomial?

Back

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