Hi,
I am planning to launch a blog where I will write about ‘finance and education’.
At the same time,I also like technology and gadgets. I know technology on a finance blog sounds odd,but if I don’t include tech and gadgets,I will be missing on building backlinks on tech blogs as they would be irrelevant. Also,a core finance blog is easier to rank for finance and educational keywords compared to a blog which has finance,education,tech and gadgets ?
Hi so what is the actual question your asking? is it about wether they go together?
Have you considered maintaining two blogs? It would probably be easier to rank each site individually than one site for both keyword groups.
I hope you are prepared for an uphill battle with the keywords you are targeting. It would take an experienced SEO and a team of writers several months to become competitive in these markets. You will be competing with lots of people who have been writing unique content and promoting their site effectively for 10+ years. Not to mention other sites like Yahoo and Forbes.
If you are going to focus on topics that don’t really go together, you may be best off adding a few more categories and making it a general news site. Either way, you may want to consider other routes of funneling traffic while your search engine authority is building up.
I would deffo agree with @alabamaseo - these are no go areas for seo because of the competition. However if you are really serious about it then there is always a way. If you are samrt about it and i’m refering to your keyword research the you are looking at 18 months for so to see ay significant ranking benefits. 
I think you should be thinking more about the people you hope will read your blog, not the search engines. There are lots of blogs that very unfocused yet have a great following. Without other people you will have a tough time, and thinking the search engines will deliver those people to you may be a little short sighted at this day and age.
It makes a lot of sense to focus on people and not robots and this is what i practice and recommend. However my people focus on the botom line so they want results and thereby take short cuts (not all people) just saying.
focus on content - actually focus on value.