Roots above the ground?

Algebra Level 3

\(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(\large\ { x }^{ 4 } - a{ x }^{ 3 } + a{ x }^{ 2 } + bx + c = 0\) where \(a, b, c\) are real numbers. What is the smallest possible value of \(\large\ { \alpha }^{ 2 } + { \beta }^{ 2 } + { \gamma }^{ 2 } + { \delta }^{ 2 }\)?

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