Question:
If w is a non-real cube root of unity, then what is a root of the following equation? x x x 1 1 1 2 2 2 = 0
If w is a non-real cube root of unity, then what is a root of the following equation? x x x 1 1 1 2 2 2 = 0
Options:
- a) x = 0
- b) x = 1
- c) x = w
- d) x = w2
- a) x = 0
- b) x = 1
- c) x = w
- d) x = w2
correct answer : a)
Explanation:
x
x
x
+
+
+
1
1
1
2
2
2
ωω
ωω
ωω
= 0
(Applying C1 ® C1 + C2 + C3)
x
xx
xx
++ +
++ ++
++ ++
1
11
11
22
22
2
ωω ωω
ωω ω
ωω ω
= 0
x
xx
xx
ωω
ω
ω
2
2 1
1
+
+
= 0
x
1
11
11
2
2
ωω
ω
ω
x
x
+
+
= 0
\ x = 0
x
x
x
+
+
+
1
1
1
2
2
2
ωω
ωω
ωω
= 0
(Applying C1 ® C1 + C2 + C3)
x
xx
xx
++ +
++ ++
++ ++
1
11
11
22
22
2
ωω ωω
ωω ω
ωω ω
= 0
x
xx
xx
ωω
ω
ω
2
2 1
1
+
+
= 0
x
1
11
11
2
2
ωω
ω
ω
x
x
+
+
= 0
\ x = 0