Respuesta :
Answer:
3 - [tex]\sqrt{11}[/tex]
Step-by-step explanation:
radical roots occur in conjugate pairs
If 3 +[tex]\sqrt{11}[/tex] is a root then so is 3 - [tex]\sqrt{11}[/tex]
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 :
[tex]0,~~4~~\textup{and}~~3+\sqrt{11}.[/tex]
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).
