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If \( \alpha \) and \( \beta \) are the roots of the equation \( a x^{2}+b x+c \) \( =0 \), then the equation whose roots are \( \alpha^{2}+\beta^{2} \) and
\( \mathrm{P} \)
\( \frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}} \), is
(1) \( a c x^{2}+b(a+c) x+(a+c)^{2}=0 \)
(2) \( a c x^{2}-\left(b^{2}-2 a c\right) x+a c=0 \)
(3) \( (a c x)^{2}-\left(b^{2}-2 a c\right)\left(a^{2}+c^{2}\right) x+\left(b^{2}-2 a c\right)^{2}=0 \)
(4) None of these


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