Question

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

Answer 1

Answer:

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

Step-by-step 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