Quality Score is not a fixed measurement
The QS (quality score) shown in your Adwords account is an indicative measure and not an absolute but is an indication of how well Google thinks you’re doing.
It is calculated, in real-time, each time a searcher enters a search query and used in the decision if your ad will be shown, what position it will appear and what each click will cost.
The importance of CTR (click-through rate)
Like most things Google it is not an easily understood measure primarily as Google keeps the formula close to its chest but CTR (click-through rate) appears to be a major contributor in terms of the historical CTR of the individual keyword and matched ad on the Google Network together with the historical CTR of all the ads and keywords in your account and the CTR of the display URLs in the specific ad group.
Relevancy of the keyword to the ad in its group and the relevancy of the keyword, the matched ad and the search query together with your account’s overall performance in the geographic area the ads are shown.
Your landing page is important but not critical!
Landing page quality is a factor but not the the degree that might be thought and far more likely to be potentially harmful rather than a positive benefit.
Landing pages are not used for Ad Rank calculation but a slow to load, ‘bad’ or deceptive landing page, missing essential privacy or contact information could lower QS and have an overall impact on CPC (cost-per-click).
The importance of a landing page is once the click has been made and its contribution to the conversion process from that point on.
What’s important? Focus on raising CTR!
Whether we regard it as right or wrong, Google considers CTR as a measure of relevancy so the objective for any Adwords campaign is to aim for a high click-through rate which in turn will contribute to a higher QS.
Matching ad text with searched for queries in small, tightly focused ad groups targeting closely related keywords will help raise CTR with a consequent benefit for QS.
There’s no magic bullet but identifying the most relevant keywords, testing ad copy and monitoring CTRs closely will help improve ad group, campaign and overall account performance and lower costs.