Quadratic Equation #9

Algebra Level 3

Let equation \[ax^{2} + bx + c = 0 \] whose roots are the reciprocals of the roots of \[x^{2} + 2x +3 = 0. \]

If \( a, b, c \) are positive integers such that \( \gcd (a, b, c) = 1 \), find \[ a + b + c. \]

Algebra Question

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