Question

Which of the following is a polynomial with roots 5, 7, and −8?

(A). f(x) = x3 − 35x2 − 56x + 61
(B). f(x) = x3 − 35x2 − 61x + 280
(C). f(x) = x3 − 4x2 − 35x + 56
(D). f(x) = x3 − 4x2 − 61x + 280

Answer 1

I think it’s D (hope I helped

Answer 2

The correct option is D.

Explanation:

According the definition of roots if a function f(x) have a root c, then (x-c) is a factor of f(x).

The function is defined as,

`f(x)=c(x-a_1)^(m_1)(x-a_2)^(m_2)...(x-a_n)^(m_n)`

Where c is a constant,
`a_1,a_2,...a_n` are roots with multiplicity
`m_1,m_2,...m_n` respectively.

It is given that the roots of the function are 5,7 and -8, therefore the factors of the polynomial are (x-5),(x-7) and (x+8).

Multiply the factors to get the function.

`f(x)=(x-5)(x-7)(x+8)`

`f(x)=(x-5)(x^2-7x+8x-56)`

`f(x)=(x-5)(x^2+x-56)`

`f(x)=x^3+x^2-56x-5x^2-5x+280`

`f(x)=x^3-4x^2-61x+280`

Therefore, the correct option is D.