Bob was asked to construct a polynomial function with the fallowing zeros and multiplicities. Which function should he write?
Zero: x=1, x=81
Multiplicity; 3, 5
f(x)=(x+1)^5(x+81)^3
f(x)=(x-1)^5(x-81)^3
f(x)=(x+1)^3(x+81)^5
f(x)=(x-1)^3(x-81)^5
3 answers
Bob should write the function f(x)=(x-1)^3(x-81)^5.
That’s wrong
Apologies for the confusion. Let's correct the answer.
To construct a polynomial function with given zeros and multiplicities, we need to use their corresponding zero-multiplicity form.
Given zeros:
x = 1, multiplicity = 3
x = 81, multiplicity = 5
The zero-multiplicity form of a polynomial function for each zero is (x - a)^n, where "a" is the zero and "n" is the multiplicity.
For the zero x = 1 with multiplicity 3, the term in the function will be (x - 1)^3.
For the zero x = 81 with multiplicity 5, the term in the function will be (x - 81)^5.
So, the correct function that Bob should write is:
f(x) = (x - 1)^3(x - 81)^5
Therefore, the correct option is:
f(x) = (x - 1)^3(x - 81)^5
To construct a polynomial function with given zeros and multiplicities, we need to use their corresponding zero-multiplicity form.
Given zeros:
x = 1, multiplicity = 3
x = 81, multiplicity = 5
The zero-multiplicity form of a polynomial function for each zero is (x - a)^n, where "a" is the zero and "n" is the multiplicity.
For the zero x = 1 with multiplicity 3, the term in the function will be (x - 1)^3.
For the zero x = 81 with multiplicity 5, the term in the function will be (x - 81)^5.
So, the correct function that Bob should write is:
f(x) = (x - 1)^3(x - 81)^5
Therefore, the correct option is:
f(x) = (x - 1)^3(x - 81)^5
2 answers