HTML 4 & CSS 3: required input needs custom background-color

I need to change background color of required inputs in a form.

Following code doesn't work:

CSS

input[type="text"] .required { background-color: yellow; }

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or CSS:

input .required { background-color: yellow; }

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HTML:

<input class="required" type="text" id="email" name="email">

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Tested in browsers FF 17.0.1 and IE 9 with latest patches.
Only HTML 4 and CSS 3 is acceptable.