Question

Which of the following is the polynomial function that has the zeroes 0, 1, 5?

A) f(x)=x(x−1)(x−5)
B) f(x)=x^2+x−5
C) f(x)=(x−1)(x−5)
D) f(x)=x(x+1)(x+5)

Answer 1

The polynomial function that has the zeroes 0, 1, and 5 is f(x) = x(x−1)(x−5).

Step-by-step explanation:

The polynomial function that has the zeroes 0, 1, 5 is f(x)=x(x−1)(x−5). Zeroes of a polynomial are the values of x for which the function equals zero. To create a polynomial that has 0, 1, and 5 as zeroes, we would multiply the linear factors associated with each zero (x for 0, (x-1) for 1, and (x-5) for 5).

The correct option is A) f(x)=x(x−1)(x−5) since this function will equal zero when x is 0, 1, or 5.The polynomial function that has the zeroes 0, 1, and 5 is given by option A) f(x) = x(x−1)(x−5).

To find the polynomial function with these zeroes, we can use the zero-product property. The zero-product property states that if a product of factors equals zero, then at least one of the factors must be zero.

Therefore, the polynomial function with zeroes 0, 1, and 5 can be written as f(x) = x(x−1)(x−5).