Question

Find the zeros and give the multiplicity of

F(x)= x^2(x^2+18x+81)

Answer 1

Explanation:

To find the zeros of F(x), we need to solve the equation F(x) = 0.

F(x) = x^2(x^2+18x+81)

The expression F(x) can be factored as:

F(x) = x^2(x+9)^2

So, the zeros of F(x) are x = 0 and x = -9, with a multiplicity of 2 for both.

The factor x^2 contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = 0 but does not cross it. The factor (x+9)^2 also contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = -9 but does not cross it.

To summarize, the zeros and their multiplicities for F(x) are:

x = 0 (multiplicity 2)

x = -9 (multiplicity 2)