Quadratic Equations And Cubic Equations Worksheet With Answers Page 3
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2
3
4
5
61
1
Given the roots 2α
and 2β
,
β
α
1
1
α + β
2α
+ 2β
= 2(α + β)
(
)
β
α
αβ
1
1
3
= 2(
)
(+
)
3
3
5
2
1
=
+
3
5
10 + 3
=
15
13
=
15
1
1
1
(2α
)(2β
) = 4αβ +
4
β
α
αβ
169
=
15
Therefore the required equation is
13
169
2
x
x
= 0
15
15
that is
2
15x
13x
169 = 0.
2
Exercise: One root of the equation 2x
+ bx + c = 0 is three times the
2
other root. Show that 3b
= 32c.
3
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