If one root of the equation \( a x^{2}+b x+c=0 \) is the square of the other, then (a) \( b^{2}+...

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If one root of the equation \( a x^{2}+b x+c=0 \) is the square of the other, then
(a) \( b^{2}+a c^{2}+a^{2} c=3 a b c \)
(b) \( b^{3}+a c^{2}+a^{2} c=3 a b c \)
(c) \( b^{2}+a c^{2}+a^{2} c+3 a b c=0 \)
(d) \( b^{3}+a c^{2}+a^{2} c+3 a b c=0 \)
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