Find alpha^-2 + beta^-2, if alpha and beta are the zeroes of the polynomial2 x^2 – X+5. About the author Cora
Step-by-step explanation: 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 Reply
Step-by-step explanation:
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