Complex Numbers and Quadratic Equations · Question 54

If the set of all a R - \1\, for which the roots of the equation (1 - a)x2 + 2(a - 3)x + 9 = 0 are positive is (- , - ] [ , ), then 2 + + is equal to .

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

Let |z1 - 8 - 2i| 1 and |z2 - 2 + 6i| 2, z1, z2 C. Then the minimum value of |z1 - z2| is :

1. 3
2. 10
3. 7
4. 13

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)

Let O be the origin, the point A be z1 = 3 + 2 2i, the point B(z2) be such that 3|z2| = |z1| and (z2) = (z1) + 6. Then

1. area of triangle ABO is 114
2. area of triangle ABO is 11 3
3. ABO is a scalene triangle
4. ABO is an obtuse angled isosceles triangle

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