Complex Numbers and Quadratic Equations

Let , be the roots of the equation x2-x+p=0 and , be the roots of the equation x2-4x+q=0; p, q Z. If , , , are in G.P., then |p+q| equals :

1. 16
2. 32
3. 34
4. 38

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

If the set of all solutions of |x2+x-9|=|x|+|x2-9| is [ , ] [ , ), then ( 2+ 2+ 2 ) is equal to:

1. 9
2. 18
3. 36
4. 72

Let z be a complex number such that |z+2|=|z-2| and ( z+3z-i )= 4. Then |z|2 is equal to:

1. 9
2. 4
3. 5
4. 1

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 the quadratic equation ( +2)x2-3 x+4 =0, -2, has two positive roots, then the number of possible integral values of is :

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

Let , +2, Z, be the roots of the quadratic equation x(x+2)+(x+1)(x+3)+(x+2)(x+4)+ +(x+n-1)(x+n+1)=4n for some n N. Then n+ is equal to :

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

Let x and y be real numbers such that 50 ( 2x1+3i- y1-2i )=31+17i, i= -1. Then the value of 10(x-3y) is :

1. 20
2. 31
3. 35
4. 75

Let , be the roots of the equation x2-3x+r=0, and 2, 2 be the roots of the equation x2+3x+r=0. If the roots of the equation x2+6x=m are 2 + +2r and -2 - r2, then m is equal to :

1. -135
2. -567
3. 135
4. 567

Let the circles C1 : |z|=r and C2 : |z-3-4i|=5, z C, be such that C2 lies within C1. If z1 moves on C1, z2 moves on C2 and |z1-z2|=2, then |z1-z2| is equal to :

1. 12
2. 17
3. 22
4. 24