[tex]x_1, x_2[/tex] and [tex]x_3[/tex] are the zeros of h(x). It means:
[tex]h(x_1)=0, h(x_2)=0 \text{ and } h(x_3)=0 .[/tex]
For [tex]c(x)=7h(x)[/tex] we have:
[tex]c(x_1) = 7 h(x_1) = 0 \\ c(x_2) = 7 h(x_2) = 0\\ c(x_3) = 7 h(x_3) =0[/tex]
So the zeros of c are the same zeros of h.
For [tex]g(x) = h(x-2)[/tex] we have:
[tex]g(x_1+2) = h(x_1+2-2) = 0 \\ g(x_2+2) = h(x_2+2-2) = 0\\ g(x_3+2) = h(x_3+2-2) =0[/tex]
So the zeros of g are [tex]x_1+2, x_2+2 and x_3+2[/tex] .
