If α and β are the two zeroes of a polynomial x2 – 5x + 6 then the

1.	If α and β are the two zeroes of a polynomial x2 – 5x + 6 then the value of 1/a2 + 1/β2 is ...............A) 13/36B) 17/36C) 19/36D) 23/36
Answer» Correct option is (A) 13/36 \(\because\) \(\alpha+\beta\) \(=\frac{-(-5)}1\) = 5 and \(\alpha\beta\) \(=\frac61\) = 6 \(\therefore\) \(\frac{\alpha+\beta}{\alpha\beta}=\frac56\) \(\Rightarrow\) \(\frac{1}{\alpha}+\frac{1}{\beta}\) \(=\frac56\) \(\therefore\) \((\frac{1}{\alpha}+\frac{1}{\beta})^2\) \(=(\frac56)^2\) \(\Rightarrow\) \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac2{\alpha\beta}\) \(=\frac{25}{36}\) \(\Rightarrow\) \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) \(=\frac{25}{36}-\frac2{\alpha\beta}\) \(=\frac{25}{36}-\frac26\) \(=\frac{25-12}{36}=\frac{13}{36}\) Correct option is A) 13/36

If α and β are the two zeroes of a polynomial x2 – 5x + 6 then the value of 1/a2 + 1/β2 is ...............A) 13/36B) 17/36C) 19/36D) 23/36

Answer»

Correct option is (A) 13/36

\(\because\) \(\alpha+\beta\) \(=\frac{-(-5)}1\) = 5 and \(\alpha\beta\) \(=\frac61\) = 6

\(\therefore\) \(\frac{\alpha+\beta}{\alpha\beta}=\frac56\)

\(\Rightarrow\) \(\frac{1}{\alpha}+\frac{1}{\beta}\) \(=\frac56\)

\(\therefore\) \((\frac{1}{\alpha}+\frac{1}{\beta})^2\) \(=(\frac56)^2\)

\(\Rightarrow\) \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac2{\alpha\beta}\) \(=\frac{25}{36}\)

\(\Rightarrow\) \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) \(=\frac{25}{36}-\frac2{\alpha\beta}\)

\(=\frac{25}{36}-\frac26\) \(=\frac{25-12}{36}=\frac{13}{36}\)

Correct option is A) 13/36