Correct option is (A) 13/36
\(\because\) \(\alpha+\beta\) \(=\frac{-(-5)}1\) = 5 and \(\alpha\beta\) \(=\frac61\) = 6
\(\therefore\) \(\frac{\alpha+\beta}{\alpha\beta}=\frac56\)
\(\Rightarrow\) \(\frac{1}{\alpha}+\frac{1}{\beta}\) \(=\frac56\)
\(\therefore\) \((\frac{1}{\alpha}+\frac{1}{\beta})^2\) \(=(\frac56)^2\)
\(\Rightarrow\) \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac2{\alpha\beta}\) \(=\frac{25}{36}\)
\(\Rightarrow\) \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) \(=\frac{25}{36}-\frac2{\alpha\beta}\)
\(=\frac{25}{36}-\frac26\) \(=\frac{25-12}{36}=\frac{13}{36}\)
