Question

if the zeroes of the polynomial ax^2+bx+b=0 are in the ratio m:n hen find the value of root m+n +root n+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

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