Complex Numbers and Quadratic Equations

The number of real solutions of the equation x|x + 5| + 2|x + 7| - 2 = 0 is .

If 2 and 6 are the roots of the equation ax2+bx+1=0, then the quadratic equation, whose roots are 12a+b and 16a+b, is :

1. x2+8x+12=0
2. 2x2+11x+12=0
3. 4x2+14x+12=0
4. x2+10x+16=0

Let and be the sum and the product of all the non-zero solutions of the equation ( z)2+|z|=0, z . Then 4( 2+ 2) is equal to :

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

The area (in sq. units) of the region S = \z C : |z - 1| 2; (z + z) + i(z - z) 2, Im(z) 0\ is

1. 7 4
2. 3 2
3. 7 3
4. 17 8

Let S = \ 2 2 : ( 4 + 4 )x2 + ( 2 )x + ( 6 + 6 ) = 0 has real roots\. If and be the smallest and largest elements of the set S, respectively, then 3 (( - 2)2 + ( - 1)2 ) equals .

Let S= \z :|z-1|=1 and ( 2-1)(z+ z)-i(z- z)=2 2 \. Let z1, z2 be such that |z1|= z S|z| and |z2|= z S|z|. Then | 2z1-z2 |2 equals :

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

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

Let P=\z C: |z+2-3i| 1\ and Q=\z C: z(1+i)+ z(1-i) -8\. Let in P , |z-3+2i| be maximum and minimum at z1 and z2 respectively. If |z1|2+2|z2|2= + 2, where , are integers, then + equals .

If z is a complex number such that |z| 1, then the minimum value of |z+ 12(3+4 i) | is :

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

Let and be the roots of the equation p x2+q x-r=0, where p 0. If p, q and r be the consecutive terms of a non constant G.P. and 1 + 1 = 34, then the value of ( - )2 is :

1. 8
2. 9
3. 203
4. 809