PYQSide ExamsMy practice

Complex Numbers and Quadratic Equations · Question 19

JEE Main 2026 (Online) 28th January Evening ShiftMCQMedium📈 Topic in 26% papers+4−1
1

Let the arithmetic mean of 1a and 1b be 516, a > 2. If is such that a, 4, , b are in A.P., then the equation x2 - ax + 2( - 2b) = 0 has :

  1. one root in (1, 4) and another in (-2, 0)
  2. one root in (0, 2) and another in (-4, -2)
  3. both roots in the interval (-2, 0)
  4. complex roots of magnitude less than 2

Answer

(1) one root in (1, 4) and another in (-2, 0)

Solution

a, 4, , b in A.P. with common difference 4 - a

= 8 - a, b = 12 - 2a

1a + 1b = 2 516 = 58

1a + 112 - 2a = 58 12 - aa(12 - 2a) = 58

96 - 8a = 60a - 10a2 5a2 - 34a + 48 = 0

(5a - 24)(a - 2) = 0 a = 245 (since a > 2)

= 165, b = 125

Equation: 165x2 - 245x + 2 ( 165 - 245 ) = 0

16x2 - 24x - 16 = 0 2x2 - 3x - 2 = 0

(x - 2)(2x + 1) = 0 x = 2, - 12

one root (2) (1, 4) and the other (- 12 ) (-2, 0)

Answer: (1)

JEE Main 2026 (Online) 28th January Evening Shift

Keep practising — Complex Numbers and Quadratic Equations

2

Let A = \z C : |z - 2| 4\ and B = \z C : |z - 2| + |z + 2| = 5\. Then the \|z1 - z2| : z1 A and z2 B\ is :

  1. 172
  2. 8
  3. 9
  4. 152
JEE Main 2026 (Online) 28th January Evening Shift
3

The number of the real solutions of the equation: x|x + 3| + |x - 1| - 2 = 0 is

  1. 3
  2. 2
  3. 5
  4. 4
JEE Main 2026 (Online) 24th January Morning Shift
4

Let S = \z C : | z-6iz-2i | = 1 and | z-8+2iz+2i | = 35 \. Then z S |z|2 is equal to :

  1. 413
  2. 398
  3. 385
  4. 423
JEE Main 2026 (Online) 24th January Morning Shift
5

The smallest positive integral value of a, for which all the roots of x4 - ax2 + 9 = 0 are real and distinct, is equal to

  1. 7
  2. 3
  3. 4
  4. 9
JEE Main 2026 (Online) 24th January Evening Shift
6

Let z = (1 + i)(1 + 2i)(1 + 3i) (1 + ni), where i = -1. If |z|2 = 44200, then n is equal to .

JEE Main 2026 (Online) 24th January Evening Shift
7

If α and β (α < β) are the roots of the equation (-2 + 3 ) ( | x - 3 | ) + (x - 6 x ) + (9 - 2 3 ) = 0, x 0, then + is equal to :

  1. 8
  2. 10
  3. 9
  4. 11
JEE Main 2026 (Online) 23rd January Morning Shift
8

Let S = \z : 3 |2z - 3(1 + i)| 7 \ be a set of complex numbers. Then Minz S | (z + 12(5 + 3i) ) | is equal to :

  1. 12
  2. 52
  3. 2
  4. 32
JEE Main 2026 (Online) 23rd January Morning Shift
9

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :

  1. 36 days
  2. 24 days
  3. 30 days
  4. 42 days
JEE Main 2026 (Online) 23rd January Morning Shift
10

If z = 32 + i2, i = -1, then (z201 - i )8 is equal to

  1. 1
  2. 0
  3. -1
  4. 256
JEE Main 2026 (Online) 23rd January Evening Shift
11

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
JEE Main 2026 (Online) 22nd January Morning Shift

All Complex Numbers and Quadratic Equations PYQs →

PDFDownload Complex Numbers and Quadratic Equations PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇
All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)