How to inject Javascript in WebBrowser control?

I've tried this:

string newScript = textBox1.Text;
HtmlElement head = browserCtrl.Document.GetElementsByTagName("head")[0];
HtmlElement scriptEl = browserCtrl.Document.CreateElement("script");
lblStatus.Text = scriptEl.GetType().ToString();
scriptEl.SetAttribute("type", "text/javascript");
head.AppendChild(scriptEl);
scriptEl.InnerHtml = "function sayHello() { alert('hello') }";

scriptEl.InnerHtml and scriptEl.InnerText both give errors:

System.NotSupportedException: Property is not supported on this type of HtmlElement.
   at System.Windows.Forms.HtmlElement.set_InnerHtml(String value)
   at SForceApp.Form1.button1_Click(Object sender, EventArgs e) in d:\jsight\installs\SForceApp\SForceApp\Form1.cs:line 31
   at System.Windows.Forms.Control.OnClick(EventArgs e)
   at System.Windows.Forms.Button.OnClick(EventArgs e)
   at System.Windows.Forms.Button.OnMouseUp(MouseEventArgs mevent)
   at System.Windows.Forms.Control.WmMouseUp(Message& m, MouseButtons button, Int32 clicks)
   at System.Windows.Forms.Control.WndProc(Message& m)
   at System.Windows.Forms.ButtonBase.WndProc(Message& m)
   at System.Windows.Forms.Button.WndProc(Message& m)
   at System.Windows.Forms.Control.ControlNativeWindow.OnMessage(Message& m)
   at System.Windows.Forms.Control.ControlNativeWindow.WndProc(Message& m)
   at System.Windows.Forms.NativeWindow.Callback(IntPtr hWnd, Int32 msg, IntPtr wparam, IntPtr lparam)

Is there an easy way to inject a script into the dom?

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.

HtmlDocument doc = browser.Document;
HtmlElement head = doc.GetElementsByTagName("head")[0];
HtmlElement s = doc.CreateElement("script");
s.SetAttribute("text","function sayHello() { alert('hello'); }");
head.AppendChild(s);
browser.Document.InvokeScript("sayHello");

(tested in .NET 4 / Windows Forms App)

Edit: Fixed case issue in function set.

Here is the easiest way that I found after working on this:

string javascript = "alert('Hello');";
// or any combination of your JavaScript commands
// (including function calls, variables... etc)

// WebBrowser webBrowser1 is what you are using for your web browser
webBrowser1.Document.InvokeScript("eval", new object[] { javascript });

What global JavaScript function eval(str) does is parses and executes whatever is written in str. Check w3schools ref here.