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Complex Numbers and Quadratic Equations · Question 58

JEE Main 2025 (Online) 28th January Morning ShiftMCQEasy📈 Topic in 35% papers+4−1
1

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)

Answer

(1) 6(2 - 2)

Solution

Case 1: x 32

x2 + 2x - 3 - 4 = 0 x2 + 2x - 7 = 0 x = -1 2 2

Only x = -1 + 2 2 1.83 satisfies x 32.

Case 2: x < 32

x2 - 2x + 3 - 4 = 0 x2 - 2x - 1 = 0 x = 1 2

Only x = 1 - 2 -0.41 satisfies x < 32.

Sum of squares = (2 2 - 1)2 + (1 - 2)2

= (9 - 4 2) + (3 - 2 2)

= 12 - 6 2 = 6(2 - 2)

Answer: (1)

JEE Main 2025 (Online) 28th January Morning Shift

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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
JEE Main 2025 (Online) 28th January Morning Shift
3

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
JEE Main 2025 (Online) 28th January Evening Shift

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