"deep-seated anger" is correct and usable in written English.
You can use it to describe a feeling of strong, intense, and longstanding anger. For example: "The deep-seated anger he felt towards his parents was rooted in years of neglect."
He's creepily close to his mother and has some deep-seated anger.
This was about respect, about a deep-seated anger at years of perceived humiliation at the hands of F.A.A. supervisors.
Both of these characters are defined by their deep-seated anger over their belief in their own ugliness.
A cut in the subsidy for bread - the proximate cause of protests in place like El-Gadarif – was merely the spark that ignited deep-seated anger and desperation.
The awful things people say and do to one another don't emanate from an impulse to make mischief so much as from a deep-seated anger and frustration.
His comments reflected deep-seated anger throughout Turkish society, as well as an official determination to press the Obama administration into making sure the resolution progresses no further.
On the downside, don't underestimate the deep seated anger with The Sun on Merseyside or the depth or longevity of Labour support there.
The unrest that has broken out reflects deep-seated popular anger.
His books are fuelled by a deep-seated moral anger about the stupid things humans do: Pratchett was so furious because he was adamant we are all capable of so much more.
Over the past year, Mr. Kostunica, who presided over a fractious coalition government with Mr. Tadic, had tapped into deep-seated Serbian anger over the independence of Kosovo, and had moved to block closer ties with the European Union.
Deep-seated voter anger over the bailouts of companies like the American International Group, Citigroup and Bank of America has fed the fears of lawmakers that any other changes in the regulatory system must include the imposition of more onerous conditions on those financial institutions whose troubles could pose problems for the markets.
