JEE Quadratic#9

Algebra Level 5

\[(x^{2}+x+2)^{2}- (a-3)(x^{2}+x+2)(x^{2}+x+1)+(a-4)(x^{2}+x+1)^{2}\]

Find the maximum integral value of \(a\) for which the expression has at least one real root (for \(x\)).

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