Question

If a polynomial function f(x)has root -2 + square root 8 and 9 what must be a factor of f(x)

Answer 1

Answer:

$(x+2-\sqrt{9}) , (x-2+\sqrt{9}) ,(x-9)$

Step-by-step explanation:

Given that f(x) is a polynomial function.

This implies that f(x) has x terms of positive integral degrees and also rational coefficients only.

Since an irrational root is given a root of f(x), we find that its conjugate also should be a root of f(x)

i.e. If $-2+\sqrt{8}$ is a root, then $-2-\sqrt{8}$ is also a root.

(Because this only when multiplied will make coefficients rational)

So the factors of f(x) should be atleast

$(x+2-\sqrt{9}) , (x-2+\sqrt{9}) ,(x-9)$

There can be other factors also but this is compulsory