Quadratic Equations And Cubic Equations Worksheet With Answers Page 5
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6Solution: From the given equation
α + β + γ = 0
αβ + βγ + γα =
7
αβγ = 1
Thus,
2
2
2
2
α
+ β
+ γ
= (α + β + γ)
2(αβ + βγ + γα)
= 0
2( 7)
= 14
2
2
2
2
2
2
2
2
2
2
α
β
+ β
γ
+ γ
α
= (αβ + βγ + γα)
2(αβ
γ + α
βγ + αβγ
)
2
= ( 7)
2αβγ(α + β + γ)
= 49
2(1)(0)
= 49
2
2
2
2
2
α
β
γ
= (αβγ)
= 1
= 1.
Hence, the required equation is
3
2
x
14x
+ 49
1 = 0.
Exercise
3
3
3
3
1. If α,β and γ are the roots of x
3x + 1 = 0, find the value of α
+ β
+ γ
.
3
2
2. If α,β and γ are the roots of the equation ax
+ bx
+ cx + d = 0, where
a = 0, show that
2
(c
2bd)
2
2
2
(αβ)
+ (βγ)
+ (γα)
=
.
a
2
5
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