For some reason Richard’s solution didn’t work on my end (insertAdjacentText failed with an exception). This however seems to work:
HtmlElement head = webBrowser1.Document.GetElementsByTagName("head")[0];
HtmlElement scriptEl = webBrowser1.Document.CreateElement("script");
IHTMLScriptElement element = (IHTMLScriptElement)scriptEl.DomElement;
element.text = "function sayHello() { alert('hello') }";
head.AppendChild(scriptEl);
webBrowser1.Document.InvokeScript("sayHello");
This answer explains how to get the IHTMLScriptElement
interface into your project.