If α and β are the zeros of the polynomial 2x²−x-1, find the value of 1/ α²+1/β²
Answers
Answered by
6
Answer:
2x
2
−4x+5
α+β=
a
−b
=
2
−(−4)
=
2
4
=2
αβ=
a
c
=
2
5
(α
2
+β
2
)=(α+β)
2
−2αβ
=4−5=−1
α
1
+
β
1
=
αβ
α+β
=
2
5
2
=
5
4
(α−β)
2
=(α
2
+β
2
)−2αβ
=−1−2(
2
5
)=−1−5
=−6
(α
3
+β
3
)=(α+β)(α
2
+β
2
−αβ)
=(2)(−1
2
−5
)
=2(
2
−7
)=−7
Similar questions