Zeros & Multiplicity

Front

What is a zero of a polynomial function?

Back

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

Front

Define multiplicity in the context of polynomial roots.

Back

Multiplicity refers to the number of times a particular root (zero) appears in a polynomial.

Front

What happens to the graph of a polynomial at a zero with odd multiplicity?

Back

The graph crosses the x-axis at a zero with odd multiplicity.

Front

What happens to the graph of a polynomial at a zero with even multiplicity?

Back

The graph bounces off the x-axis at a zero with even multiplicity.

Front

Identify the zeros of the polynomial function: y = (x + 3)(x - 2)(x - 5)^2.

Back

The zeros are -3, 2, and 5 (with multiplicity 2).

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What is the significance of the multiplicity of a root?

Back

The multiplicity of a root affects the shape of the graph at that root.

Front

If a polynomial has a root of 4 with multiplicity 3, what does this imply about the graph?

Back

The graph will touch the x-axis at x = 4 and turn around, creating a 'bounce' effect.

Front

What are the roots of the polynomial function: y = x^2 - 9?

Back

The roots are 3 and -3.

Front

Explain how to determine the multiplicity of a root from a polynomial equation.

Back

The multiplicity can be determined by the exponent of the factor associated with the root.