So x² + 5x +4 has already a perfect equation for making roots how do we not we need to do complete square in it ??

We don’t need to, it’s just another method. If you can factorise, I would always go for that approach

You don’t need it for finding roots. But what if you want to maximise/minimise the quadratic?

You can find the roots from factorising and take the mean average/halfway point right?

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