Question

I need help in this please! thank you so much!

Answer 1

C) p(x) has a zero between x=2 and x=4

Explanation:

For a polynomial p(x),
`p(a)=R` means that, when p(x) is divided by
`x-a`, the remainder is
`R`.

This is called the remainder theorem

Therefore
`p(2)=1`,
`p(4)=-1` means that when p(x) is divided
`x-2` and
`x-4` is 1 and
`-1` respectively.

Also the Intermediate value theorem says that, if p(a) and p(b) have opposite signs then there is a certain
`c` on
`(a,b)` where
`f(c)=0` i.e there is a zero between
`a` and
`b`

Therefore the correct answer is C