Question

The equation whose roots are A.M and twice the H.M between the roots of the equation x^2+ax-b=0 is

Answer 1

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

Answer 2

Answer:

2ax^2+(a^2 -8b)x -4ab

Step-by-step explanation:

let the roots be A,B

A+B=-a

AB=-b

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

HM=2AB/A+B=2b/a

AM,2HM are the roots of unknown equation

x^2+(AM+2HM)x+AM*2HM

=2a^2-(a^2-8b)x-4ab=0