Question

The equation whose roots are the arithematic mean and twice the harmonic mean between the roots of the equation x^2+ax-b

Answer 1

Answer:

Let A and B are the roots of given equation .

A + B = -(a)/1 = -a

AB = -c/1 = -b

now ,

AM = ( A + B)/2 = (-a)/2

and HM = 2AB/(A + B)= 2(-b)/(-a) = 2b/a

now, a/c to question ,

AM and 2HM are the roots of unknown equation .

so,

x² -(AM +2HM)x +2(AM).(HM) =0

x²-(-a -2b)x +2(-a)(-b) =0

x² +(a +2b)x +2ab =0