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

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 :

$0,~~4~~\textup{and}~~3+\sqrt{11}.$

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).

Answer 2

Answer:

3 - $\sqrt{11}$

Step-by-step explanation:

radical roots occur in conjugate pairs

If 3 +$\sqrt{11}$ is a root then so is 3 - $\sqrt{11}$