2.If Alpha and beta are the zeroes of the polynomials ax^2+ bx + c, then find the other
polynomial whose zeroes are
Alpha square/ beta and beta square/ Alpha.
Answers
Answered by
5
Step-by-step explanation:
Sum of the roots of the given equation =α+β=
a
−b
...(1)
Product of the roots of the given equation =αβ=−
a
c
....(2)
β
α
2
+
α
β
2
=
αβ
α
3
+β
3
=
αβ
(α+β)(α
2
−αβ+β
2
)
=
αβ
(α+β)((α+β)
2
−2αβ−αβ)
=
αβ
(α+β)((α+β)
2
−3αβ)
....(3)
Substituting (1),(2) in (3), we get
β
α
2 +
α
β
2
=
−c/a
(−b/a)((−b/a)
2
−3(−c/a))
Answered by
1
Answer:
Sum of the roots of the given equation =α+β=
a
−b
...(1)
Product of the roots of the given equation =αβ=−
a
c
....(2)
β
α
2
+
α
β
2
=
αβ
α
3
+β
3
=
αβ
(α+β)(α
2
−αβ+β
2
)
=
αβ
(α+β)((α+β)
2
−2αβ−αβ)
=
αβ
(α+β)((α+β)
2
−3αβ)
....(3)
Substituting (1),(2) in (3), we get
β
α
2
+
α
β
2
=
−c/a
(−b/a)((−b/a)
2
−3(−c/a))
=
c
b
[
a
2
b
2
+
a
3c
]=
c
b
a
2
b
2
+3abc
=
a
2
c
b
3
+3abc
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