if the arithmetic mean of the roots of eqn x(x-2)+4ax=5 fond the value of a
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Answer
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
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