Question

If the zeroes of the polynomial ax2+bx+b=0 are in the ratio m:n, then find the value of root m/ root n + root n/root m.

Answer 1

let the zeros of the given polynomial ax^2+bx+c be m"alpha" and n"alpha"

m "alpha " + n"alpha" = -b/a
=>"alpha"= -b/a(m+n)------------------(i)

and similarly product of zeros 
=> mn"alpha^2"=b/a-------------(ii)

Now,

Putting the value of equation (i) in equation (ii)
You would get the desired answer which is 

root m/ root n +root n/root m
=>root b/a

Answer 2

Answer:

let the zeros of the given polynomial ax^2+bx+c be m"alpha" and n"alpha"

m "alpha " + n"alpha" = -b/a

=>"alpha"= -b/a(m+n)------------------(i)

and similarly product of zeros 

=> mn"alpha^2"=b/a-------------(ii)

Now,

Putting the value of equation (i) in equation (ii)

You would get the desired answer which is 

root m/ root n +root n/root m

=>root b/a