Answer:
C) p(x) has a zero between x=2 and x=4
Step-by-step explanation:
For a polynomial p(x), [tex]p(a)=R[/tex] means that, when p(x) is divided by [tex]x-a[/tex], the remainder is [tex]R[/tex].
This is called the remainder theorem
Therefore [tex]p(2)=1[/tex], [tex]p(4)=-1[/tex] means that when p(x) is divided [tex]x-2[/tex] and [tex]x-4[/tex] is 1 and [tex]-1[/tex] respectively.
Also the Intermediate value theorem says that, if p(a) and p(b) have opposite signs then there is a certain [tex]c[/tex] on [tex](a,b)[/tex] where [tex]f(c)=0[/tex] i.e there is a zero between [tex]a[/tex] and [tex]b[/tex]
Therefore the correct answer is C
