Question

If α and β are the zeroes of x2 + px + q then find the value of α/β +2 ×β/α+2

Answer 1

Answer:

$(\alpha /\beta +2)(\beta /\alpha +2)\\(\alpha +2\beta /\beta )(\beta +2\alpha /\alpha )\\(\alpha \beta +2\alpha^{2}+2\beta^{2} +4\alpha \beta )/\alpha \beta \\2(\alpha^{2} +\beta^{2} +2\alpha \beta )+\alpha \beta )/\alpha\beta \\(2(\alpha +\beta )^{2} +\alpha \beta )/\alpha \beta \\\alpha +\beta =-b/a=-p/1=-p\\\alpha \beta =c/a=q/1=q\\(2(-p)^{2} q)/q\\(2p^{2} +q)/q$

∴ans=$(2p^{2} +q)/q$