Complex Numbers and Quadratic Equations

If α and β (α < β) are the roots of the equation (-2 + 3 ) ( | x - 3 | ) + (x - 6 x ) + (9 - 2 3 ) = 0, x 0, then + is equal to :

1. 8
2. 10
3. 9
4. 11

Let S = \z : 3 |2z - 3(1 + i)| 7 \ be a set of complex numbers. Then Minz S | (z + 12(5 + 3i) ) | is equal to :

1. 12
2. 52
3. 2
4. 32

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :

1. 36 days
2. 24 days
3. 30 days
4. 42 days

If z = 32 + i2, i = -1, then (z201 - i )8 is equal to

1. 1
2. 0
3. -1
4. 256

The number of distinct real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 is

1. 2
2. 3
3. 0
4. 1

Let = -1 + i 32 and = -1 - i 32, i = -1. If (7 - 7 + 9 )20 + (9 + 7 - 7 )20 + (-7 + 9 + 7 )20 + (14 + 7 + 7 )20 = m10, then m is

Let , be the roots of the quadratic equation 12x2 - 20x + 3 = 0, Z. If 12 | - | 32, then the sum of all possible values of is :

1. 3
2. 6
3. 1
4. 4

Let S = \z C : 4z2 + z = 0\. Then z S |z|2 is equal to:

1. 564
2. 116
3. 764
4. 316

If x2 + x + 1 = 0, then the value of (x + 1x )4 + (x2 + 1x2 )4 + (x3 + 1x3 )4 + + (x25 + 1x25 )4 is:

1. 162
2. 145
3. 128
4. 175

The sum of all the roots of the equation (x - 1)2 - 5|x - 1| + 6 = 0, is :

1. 3
2. 1
3. 4
4. 5