Tricky Quartic!

Algebra Level 4

(x2+3x+7)(x2+5x+2)=0(x^{2}+3x + 7)(x^{2}+5x+2)=0 If α\alpha, β\beta, γ\gamma, and δ\delta are the roots of equation above, then find (α2+1)(β2+1)(γ2+1)(δ2+1).(\alpha ^{2}+1)(\beta ^{2}+1)(\gamma ^{2}+1)(\delta ^{2}+1).

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