α + ß = \(\frac{-b}a=\frac{-5}k\)
αß = \(\frac ca=\frac 2k\)
Now, \(\frac1{\alpha^2} + \frac1{\beta^2}\) = \(\frac{\alpha^2+\beta^2}{(\alpha\beta)^2}=\frac{(α+\beta)^2-2\alpha\beta}{(\alpha\beta)^2}\)
= \(\cfrac{(\frac{-5}k)^2-4/k}{(\frac 2k)^2}\) = \(\cfrac{\frac{25}{k^2}-\frac 4k}{\frac4{k^2}}\)
= \(\frac{25-4k}4=\frac{17}4\)
⇒ 25 - 4k = 17
⇒ 4k = 25 - 17 = 8
⇒ k = 2
