Question

Find all zeros of ƒ(x) = x^3 + 2x^2 – x – 2. Then determine the multiplicity at each zero. State whether the graph will touch or cross the x-axis at the zero.

Answer 1

The zeros of the function ƒ(x) = x^3 + 2x^2 – x – 2 are x = -2, x = 1, and x = -1, each with a multiplicity of 1. The graph will cross the x-axis at each zero.

Step-by-step explanation:

To find the zeros of the function ƒ(x) = x^3 + 2x^2 – x – 2, we set the function equal to zero and solve for x. By factoring, we find that (x+2)(x-1)(x+1) = 0. Therefore, the zeros of the function are x = -2, x = 1, and x = -1.

The multiplicity of a zero refers to the number of times the factor appears in the factored form of the function. In this case, each zero has a multiplicity of 1, since each factor appears once.

The graph of the function will cross the x-axis at each zero, because the multiplicity of each zero is 1.