Complex Numbers and Quadratic Equations

Let z1, z2 C be the distinct solutions of the equation z2+4z-(1+12i)=0. Then |z1|2+|z2|2 is equal to :

1. 18
2. 22
3. 29
4. 34

Let S=\z C : z2+4z+16=0\. Then z S |z+ 3 i |2 is equal to :

1. 42
2. 23
3. 27
4. 38

If α, β, where α < β, are the roots of the equation x2 - ( + 3)x + 3 = 0 such that 1 - 1 = 13, then the sum of all possible values of λ is

1. 2
2. 6
3. 8
4. 4

The number of the real solutions of the equation: x|x + 3| + |x - 1| - 2 = 0 is

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

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

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

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

The sum of the squares of the roots of |x-2|2 + |x-2| - 2 = 0 and the squares of the roots of x2 - 2|x-3| - 5 = 0, is

1. 24
2. 26
3. 36
4. 30

The number of real roots of the equation x|x-2| + 3|x-3| + 1 = 0 is :

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

The number of solutions of the equation ( 9x - 9 x + 2 ) ( 2x - 7 x + 3 ) = 0 is :

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

The sum, of the squares of all the roots of the equation x2 + |2x - 3| - 4 = 0, is

1. 6(2 - 2)
2. 3(3 - 2)
3. 3(2 - 2)
4. 6(3 - 2)

If + i and + i are the roots of x2 - (3 - 2i)x - (2i - 2) = 0, i = -1, then + is equal to:

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

If and are the roots of the equation 2z2-3z-2i=0, where i= -1, then 16 ( 19+ 19+ 11+ 11 15+ 15 ) ( 19+ 19+ 11+ 11 15+ 15 ) is equal to

1. 441
2. 312
3. 409
4. 398

The sum of all the solutions of the equation (8)2x - 16 (8)x + 48 = 0 is :

1. 1 + 8(6)
2. 1 + 6(8)
3. 8(6)
4. 8(4)

Let S= \x :( 3+ 2)x+( 3- 2)x=10 \. Then the number of elements in S is :

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