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A resolution is an agreement made at a meeting conducted with the aim of making changes to the company. This may be a meeting of the directors to issue more shares in the company or the shareholders resolving to change the company name.
In most companies, each member has one vote per share they hold. If the majority of the shareholders eligible to vote do so in favour of the change, the resolution can be passed, if they vote against the motion, the resolution cannot be passed.
The company must circulate notice of the intention to propose a resolution to its members. If a company has auditors, it must send copies or otherwise notify them of the contents of all proposed resolutions. The Companies Act 2006 requires that you deliver certain resolutions (for example any special resolution) to Companies House within 15 days of passing them.