2 points
IF α & β are the roots of the the quadratic equation 3m² + 2m- 4 = 0 then α²+ β²
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Answer:
Given that α,β are the roots of equation ax
2
+bx+c=0
So we have α+β=−
a
b
and αβ=
a
c
1.
α
2
1
+
β
2
1
=
(αβ)
2
α
2
+β
2
=
(αβ)
2
(α+β)
2
−2αβ
=
c
2
b
2
−2ca
2. α
4
β
7
+α
7
β
4
=(αβ)
4
(α
3
+β
3
)
=(αβ)
4
(α+β)(α
2
+β
2
−αβ)
=
a
4
c
4
×(−
a
b
)×(
a
2
b
2
−3ac
)
=
a
7
bc
4
(3ac−b
2
)
3. (
β
α
−
α
β
)
2
=(
αβ
(α+β)(α−β)
)
2
=
c
2
b
2
×(
a
2
b
2
−4ac
)
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