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Complex Numbers and Quadratic Equations · Question 29

JEE Main 2026 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 10% papers+4−1
1

The number of distinct real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 is

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

Answer

(4) 1

Solution

Case 1: x -2

x(x+4) + 3(x+2) + 10 = 0 x2 + 7x + 16 = 0

D = 49 - 64 < 0 no real root.

Case 2: -4 x < -2

x(x+4) - 3(x+2) + 10 = 0 x2 + x + 4 = 0

D = 1 - 16 < 0 no real root.

Case 3: x < -4

-x(x+4) - 3(x+2) + 10 = 0 x2 + 7x - 4 = 0

x = -7 652

x = -7 - 652 -7.53 (accepted, < -4); x = -7 + 652 0.53 (rejected)

Number of distinct real solutions = 1

Answer: (4)

JEE Main 2026 (Online) 22nd January Morning Shift

Keep practising — Complex Numbers and Quadratic Equations

2

Let = -1 + i 32 and = -1 - i 32, i = -1. If (7 - 7 + 9 )20 + (9 + 7 - 7 )20 + (-7 + 9 + 7 )20 + (14 + 7 + 7 )20 = m10, then m is

JEE Main 2026 (Online) 22nd January Morning Shift
3

Let , be the roots of the quadratic equation 12x2 - 20x + 3 = 0, Z. If 12 | - | 32, then the sum of all possible values of is :

  1. 3
  2. 6
  3. 1
  4. 4
JEE Main 2026 (Online) 22nd January Evening Shift
4

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

  1. 564
  2. 116
  3. 764
  4. 316
JEE Main 2026 (Online) 22nd January Evening Shift
5

If x2 + x + 1 = 0, then the value of (x + 1x )4 + (x2 + 1x2 )4 + (x3 + 1x3 )4 + + (x25 + 1x25 )4 is:

  1. 162
  2. 145
  3. 128
  4. 175
JEE Main 2026 (Online) 21st January Morning Shift
6

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
JEE Main 2026 (Online) 21st January Morning Shift
7

Let and be the roots of the equation x2 + 2ax + (3a + 10) = 0 such that < 1 < . Then the set of all possible values of a is :

  1. (- , -115 ) (5, )
  2. (- , -115 )
  3. (- , -3)
  4. (- , -2) (5, )
JEE Main 2026 (Online) 21st January Evening Shift
8

Let z be the complex number satisfying |z - 5| 3 and having maximum positive principal argument. Then 34 | 5z - 125iz + 16 |2 is equal to:

  1. 20
  2. 26
  3. 12
  4. 16
JEE Main 2026 (Online) 21st January Evening Shift
9

Let be a solution of x2 + x + 1 = 0, and for some a and b in R, bmatrix 4 & a & b bmatrix bmatrix 1 & 16 & 13 \ -1 & -1 & 2 \ -2 & -14 & -8 bmatrix = bmatrix 0 & 0 & 0 bmatrix. If 4 4 + m a + n b = 3, then m + n is equal to

  1. 11
  2. 3
  3. 8
  4. 7
JEE Main 2025 (Online) 8th April Evening Shift
10

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
JEE Main 2025 (Online) 8th April Evening Shift
11

Let A = \ [0, 2 ] : 1 + 10 Re ( 2 + i - 3i ) = 0 \. Then A 2 is equal to

  1. 214 2
  2. 6 2
  3. 274 2
  4. 8 2
JEE Main 2025 (Online) 8th April Evening Shift

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