If \( x^{2}+3 x+5=0 \) and \( a x^{2}+b x+c=0 \) have common root/roots and \( a, b, c \in N \) ...

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If \( x^{2}+3 x+5=0 \) and \( a x^{2}+b x+c=0 \) have common root/roots and \( a, b, c \in N \) then find the minimum value of \( a+b+c \)
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