Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 6
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34Number and Algebra
Number and Algebra
+ 5x + 6 = 0.
2
21. (a) Solve x
+ 5x + 6 = 0.
2
(b) Find a quadratic equation in x whose roots are 2 and the sum of the roots of x
Solution
+
+
=
2
(a)
x
5
x
6
0
+
+
=
(
x
2
)(
x
3
)
0
+
=
+
=
x
2
0
or
x
3
0
= −
= −
x
2
or
x
3
+ 5 x + 6 = 0 is (−2) + (−3) = −5.
2
(b)
Sum of the roots of x
∴
=
= −
x
2
or
x
5
−
=
+
=
x
2
0 or
x
5
0
−
+
=
∴ (
x
2
)(
x
5
)
0
+
−
=
2
x
3
x
10
0
∴ The required equation is x
+ 3 x − 10 = 0.
2
+
−
=
2
22. If the roots of x
have the same numerical value but different signs, find the
bx
1
0
value of b.
Solution
Let a and − a be the roots of x
+ bx − 1 = 0.
2
+
−
=
−
+
2
x
bx
1
(
x
a x
)(
a
)
=
−
2
2
x
a
∴ b = 0
6
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