If α and β are zeroes of the polynomial 2x^2-3x-9. Form a quadratic polynomial whose zeroes are 1/α^2 + 1/ β^2
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Answer:
Correct option is
A
49x
2
+18x+4
2x
2
+3x+7=0
α+β=
2
−3
αβ=
2
7
Sum of zeros =
α
2
1
+
β
2
1
=
α
2
β
2
α
2
+β
2
=
(αβ)
2
(α+β)
2
−2αβ
=
(
2
7
)
2
(
2
−3
)
2
−(2×
2
7
)
2
=
4
49
4
9
−7
=−
49
18
Product of zeros =
α
2
β
2
1
=
(
2
7
)
2
1
=
49
4
∴ The polynomial is as follows:
x
2
+(
49
18
)x+
49
4
=0
∴49x
2
+18x+4=0
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