If the zeros of the polynomial ax²+bx+b=0 are in the ratio m:n then find the value of √(m/n)+√(n/m).

If the zeros of the polynomial ax²+bx+b=0 are in the ratio m:n then f

1.	If the zeros of the polynomial ax²+bx+b=0 are in the ratio m:n then find the value of √(m/n)+√(n/m).
Answer» Let α and β are two zeroes of the polynomial ax²+bx+b.Sum of zeroes = -(b)/a = α+βProduct of zeroes = c/a = αβ = b/aα/β = m/nNow, √m/n + √n/m =√α/β + √β/α =√α/√β + √β/√α =(α+β)/√αβ =(-b/a)/√b/a =-√b/√a Question : If the zeros of the polynomial ax²+bx+b=0 are in the ratio m:n then find the value of √(m/n)+√(n/m) .Answer :ORlet the zeros of the given polynomial ax^2+bx+c be m"alpha" and n"alpha"\xa0m "alpha " + n"alpha" = -b/a=>"alpha"= -b/a(m+n)------------------(i)\xa0and similarly product of zeros\xa0=> mn"alpha^2"=b/a-------------(ii)\xa0Now,\xa0Putting the value of equation (i) in equation (ii)You would get the desired answer which is\xa0\xa0root m/ root n +root n/root m=>root b/a\xa0