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In the quadratic equation \( a x^{2}+b x+c=0, a \neq 0, \Delta=b^{2}-4 a c \) and \( \alpha+\beta, \alpha^{2}+\beta^{2}, \alpha^{3}+\beta^{3} \) are in G.P. where \( \alpha, \beta \) are the root of \( a x^{2}+b x+c=0 \), then prove that \( c \Delta=0 \)
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