If a and b are the roots of the equation 4x^2-5x+2=0,the quadratic equation with roots a^2/b,b^2/a
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Step-by-step explanation:
4x
2
−5x+2=0
Here, a=4,b=−5,c=2
α+β=
a
−b
=−
4
−5
=
4
5
and αβ=
a
c
=
4
2
=
2
1
Roots are α+
a
1
and β+
β
1
α+
α
1
+β+
β
1
=α+β+
α
1
+
β
1
=α+β+
αβ
β+α
=
4
5
+[
4
5
÷
2
1
]
=
4
5
+
2
5
=
4
15
....(1)
(α+
α
1
)(β+
α
1
)=αβ+
β
α
+
α
β
+
αβ
1
=αβ+
αβ
1
+
αβ
α
2
+β
2
α
2
+β
2
=(α+β)
2
−2αβ
=(
4
5
)
2
−2(
2
1
)=
16
25
−1=
16
9
∴αβ+
αβ
1
+
αβ
α
2
+β
2
=
2
1
+[1÷
2
1
]+
16
9
÷
2
1
∴x
2
−
4
15
x+
8
29
=0 ... from (1) and (2)
∴8x
2
−30x+29=0 (multiplying by 8)
Hence the required equation is 8x
2
−30x+29=0
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