Question

If the arithmetic mean of the roots of the equation x(x-2)+4ax=5 is 3 ,then find the value of a

Answer 1

Let the roots be α,β Hence α+β2 = 85 α + β = 165 ...(i)And 1α+ 1β2 = 87 α+βα.β = 167 α + β = 167(α.β) 165 = 167(α.β) ...from i α.β ...

Answer 2

Step-by-step explanation:

:

Let the roots be α,β

Hence

2

α+β

=

5

8

α+β=

5

16

...(i)

And

2

α

1

+

β

1

=

7

8

α.β

α+β

=

7

16

α+β=

7

16

(α.β)

5

16

=

7

16

(α.β) ...from i

α.β=

5

7

...(ii)

Thus the equation is

(x−α)(x−β)=0

x

2

−(α+β)x+α.β=0

x

2

−(

5

16

)x+

5

7

=0

5x

2

−16x+7=0