if the arithmetic mean of the roots of the equation x(x-2)+4ax=5 is 3 ,then find the value of a
please answer fast
Answers
Answered by
4
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
Answered by
2
Answer:
Let the two roots be α and β
∴
2
α+β
=8 (AM of a and b is
2
a+b
) ⟶(1)
and
αβ
=5 (GM of a and b is
ab
) ⟶(2)
From (1)
α+β=16
⇒ sum of roots =α+β=16
From (2)
αβ
=5
⇒αβ=25
∴ Products of roots =25
Now, we know that if we have the sum of roots and product of roots then the quadratic equation is given by
x
2
− (sum of the roots)x + (product of the roots) =0
∴ the quadratic equation with roots α,β are
x
2
−(α+β)x+αβ=0
x
2
−16x+25=0
Similar questions