Question

How does the multiplicity of a zero affect the graph of the polynomial function? Select answers from the drop-down menus to correctly complete the statements.

The zeros of a seventh degree polynomial function are 1, 2 (multiplicity of 3), 4, and 6 (multiplicity of 2).
The graph of the function will cross through the x-axis at ?. The graph will only touch (be tangent to) the x-axis at ?. At the zero of 2, the graph of the function will ? the x-axis.

Answer 1

Answer:

3 points: x = 1, x = 2 and x = 4

1 point: x = 6

Cross

Step-by-step explanation:

Points to remember:

• A zero of odd multiplicity will cross through the x-axis
• A zero of event multiplicity will only touch the axis i.e. be tangent to it.

The given zeros are:

• 1 with multiplicity of 1 (Odd Multiplicity)
• 2 with multiplicity of 3 (Odd Multiplicity)
• 4 with multiplicity of 1 (Odd Multiplicity)
• 6 with multiplicity of 2 (Even Multiplicity)

The graph will cross x-axis at zeros with odd multiplicity. Since zeros with odd multiplicity are 3, the graph will cross the x-axis at 3 points: x = 1, x = 2 and x = 4

Similarly, the zero of even multiplicity is 1, so the graph will touch the x-axis at 1 point only: x = 6

At the zero of 2, the graph of the function will cross the x-axis.