Question

If a polynomial function f(x) has roots 0, 4, and 3+ the square root of 11, what must also be a root of f(x)

Answer 1

3 -
`√(11)`

Explanation:

radical roots occur in conjugate pairs

If 3 +
`√(11)` is a root then so is 3 -
`√(11)`

Answer 2

Answer: (3 - √11) is also a root of the polynomial f(x).

Step-by-step explanation: Given that a polynomial function f(x) has the following roots :

`0,~~4~~\textup{and}~~3+√(11).`

We are to find the value that must also be a root of f(x).

We know that

the irrational roots of a polynomial function always occur n pairs.

That is,

(a + b√c) is a root of a polynomial P(x), then its conjugate (a - b√c) will also be a root of P(x).

Given that

(3 + √11) is a root of the polynomial f(x), so we must have

the conjugate (3 - √11) is also a root of the polynomial f(x).

Thus, (3 - √11) is also a root of the polynomial f(x).