Question

What are the zeros of the function y=(x-2)(x+7)^3 and what are their multiplicities?

a) 2, multiplicity 2; 7, multiplicity 3
b) 2, multiplicity 3; 7, multiplicity 3
c) 2, multiplicity 1; -7, multiplicity 2
d) 2, multiplicity 1; -7, multiplicity 3

Answer 1

The correct answer is D.

Answer 2

The zeros of the function y=(x-2)(x+7)^3 are 2 and -7, with multiplicities of 2 and 3 respectively.

Step-by-step explanation:

The zeros of the function y=(x-2)(x+7)^3 are the values of x that make y equal to zero. To find the zeros, we set y equal to zero and solve for x:

(x-2)(x+7)^3=0

Setting each factor equal to zero, we have:

x-2=0 → x=2

x+7=0 → x=-7

Therefore, the zeros of the function are x = 2 and x = -7.

The multiplicity of each zero is determined by the power to which the corresponding factor is raised. In this case, the factor (x-2) has a multiplicity of 1, and the factor (x+7) has a multiplicity of 3.

Therefore, the correct answer is a) 2, multiplicity 2; 7, multiplicity 3.