Recall that:
1) The zeros of a polynomial function of the form:
[tex]p(x)=(x-a_1)\cdot\ldots\cdot(x-a_n)[/tex]
are:
[tex]a_1,\ldots,a_n\text{.}[/tex]
2) The set of zeros of a rational function of the form:
[tex]r(x)=\frac{(x-a_1)\cdot\ldots\cdot(x-a_n)}{(x-b_1)\cdot\ldots\cdot(x-b_m)}[/tex]
is:
[tex]\mleft\lbrace a_1,\ldots,a_n\mright\rbrace\text{ \backslash }\mleft\lbrace b_1,\ldots,b_m\rbrace\mright?.[/tex]
Therefore the zeros of F(x) are a and b, the zeros of T(x) are c and d.
Finally, since
[tex]a\ne b\ne c\ne d,[/tex]
then the zeros of J(x) are a and b.
Answer: F(x) and J(x) have the same set of zeros.
