Technically you will still have the same zoom. "Zoom" is an all too common misunderstanding for people unfamiliar with cameras. If you look on the front of your H9 on the lens barrel you'll see "2,7-4,5/5,2-78"
The commas are supposed to be periods, so 2.7 - 4.5 / 5.2 - 78. The 2.7 - 4.5 are your maximum aperture values at 5.2mm and 78mm, respectively. They should be written as f/2.7 and f/4.5. The 5.2 - 78mm is your lens' focal length range, which determines how close or far you can make something appear. This lens is a 5.2 - 78mm zoom lens. A smaller focal length number corresponds to more of a wideangle. A larger focal length number corresponds to more of a telephoto. The 15x is simply 78mm / 5.2mm, or the zoom factor from wideangle to telephoto.
If you add a 1.7x telephoto converter (TC) your focal length range will become 8.84mm - 132.6mm (5.2 x 1.7 and 78 x 1.7). Note that this is still a 15x zoom (132.6 / 8.84 = 15). The difference though is that now your focal length has been increased by a factor of 1.7x, meaning your lens has become more of a telephoto, and can make things appear closer by a factor of 1.7x. So you've gained more reach with your telephoto end but you've lost some of the wideness of your wide end.
Also note that this 1.7x TC will make your maximum aperture smaller, effectively making it harder for your lens to gather sufficient light for a good photo. The f/2.7 - f/4.5 will now be f/4.59 and f/7.65 (larger f-values mean smaller aperture sizes)
All this is probably very confusing to you. It would make more sense if you started out by learning what aperture and focal length really are.