JEE Main · Maths · Complex Numbers and Quadratic Equations
Quadratic Roots: JEE Main previous year questions
104 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 38 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 104
- in 84 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.9
- model; history: 0.9 a shift on average, typically 0.7–1.1
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 84 of 108 shifts: 104 questions, #4 of 196 topics. It came in every year with analysed shifts.
- 02
26% of its questions since 2020 tested an idea no earlier year had asked; 61 repeated an idea from the year before.
- 03
The most repeated idea is Newton's Sums, asked 16 times in 16 shifts (2020, 2021, 2022, 2023, 2024, 2025, 2026), most often as “value from roots of linked quadratics”.
- 04
JEE Main has asked 22 of the 64 ideas in this topic; 36 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (66%); 33% need a numerical answer, 14% are easy and 19% hard.
- 06
The skill tested most is multi-step (70%), then calculation (18%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 1 in 1 shift · 2020: 13 in 12 shifts · 2021: 23 in 24 shifts · 2022: 21 in 24 shifts · 2023: 8 in 12 shifts · 2024: 20 in 18 shifts · 2025: 6 in 8 shifts · 2026: 12 in 9 shifts.
- Up to 2023
- 0.8
- a shift, of 25
- Since 2024
- 1.0
- 0.2
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 84/108
- 78% of analysed shifts
Recent framings
- quadratic root ratio then conic latus rectum
- value from roots of linked quadratics
- numerical: sum of powers of quadratic roots
Revise first
- Root-Coefficient Relation · asked 2020, 2022, 2023, 2024, 2025, 2026
- Newton's Sums · asked 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Roots of Modulus Quadratics · asked 2020, 2021, 2022, 2023, 2024, 2025
How it is asked
Difficulty, format and skill
Across all 104 questions on Quadratic Roots since 2017.
Difficulty
QUESTIONS- Easy15 · 14%
- Medium69 · 66%
- Hard20 · 19%
Format
SHARE- Single correct · 69 Q66%
- Numerical value · 34 Q33%
- Two statements · 1 Q1%
Skill tested
SHARE- Multi-step · 73 Q70%
- Calculation · 19 Q18%
- Application · 12 Q12%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 22 of the 64 ideas in this topic. 36 have never been asked yet.
- Asked directly22 · 34%
- Touched inside another question6 · 9%
- Never asked36 · 56%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
19 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
22 different ideas were tested; 13 came more than once.
value from roots of linked quadratics
Single correct · 16 shifts · 7 numericalvalue from roots of linked quadratics
Single correct · 14 shifts · 2 numericalvalue from roots of linked quadratics
Single correct · 12 shifts · 2 numericalcount real roots of modulus equation
Numerical value · 12 shifts · 6 numericalcount real roots of exponential equation
Single correct · 11 shifts · 2 numericalrange of x from discriminant condition
Numerical value · 9 shifts · 5 numericalsum of moduli over roots
Single correct · 4 shiftsvalue from roots of linked quadratics
Numerical value · 5 shifts · 3 numericalprobability of quadratic positivity condition
Numerical value · 2 shifts · 1 numericalvalue from roots of linked quadratics
Single correct · 2 shiftsvalue of high-power root expression
Numerical value · 2 shifts · 2 numericalinteger roots of quadratic from series expression
Numerical value · 2 shifts · 1 numericalquadratic with transformed roots from given roots
Single correct · 2 shiftsquadratic root ratio then conic latus rectum
Single correct · 1 shiftminimise parabola vertex distance from axis
Single correct · 1 shiftrange of rational function then symmetric sum
Single correct · 1 shiftcount parameter values for always-negative quadratic
Single correct · 1 shiftstatement i/ii on quadratic roots and means
Two statements · 1 shiftsum of roots of modulus equation
Single correct · 1 shiftdifference of roots from ap and modulus conditions
Numerical value · 1 shift · 1 numericalsum of modulus of non-real roots
Numerical value · 1 shift · 1 numericalintegral parameter for real roots of reducible equation
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Newton's Sumsvalue from roots of linked quadratics | 16 | 16 | Single correctMulti-step | 7 | |
| Root-Coefficient Relationvalue from roots of linked quadratics | 15 | 14 | Single correctMulti-step | 2 | |
| Symmetric Functionsvalue from roots of linked quadratics | 12 | 12 | Single correctMulti-step | 2 | |
| Roots of Modulus Quadraticscount real roots of modulus equation | 12 | 12 | Numerical valueMulti-step | 6 | |
| Exponential Reducible to Quadraticcount real roots of exponential equation | 11 | 11 | Single correctMulti-step | 2 | |
| Nature of Rootsrange of x from discriminant condition | 9 | 9 | Numerical valueMulti-step | 5 | |
| Complex Conjugate Rootssum of moduli over roots | 5 | 4 | Single correctMulti-step | – | |
| Common Root Conditionvalue from roots of linked quadratics | 5 | 5 | Numerical valueMulti-step | 3 | |
| Always Positive Conditionprobability of quadratic positivity condition | 2 | 2 | Numerical valueApplication | 1 | |
| Equation Formationvalue from roots of linked quadratics | 2 | 2 | Single correctCalculation | – | |
| Higher Degree Evaluation via Root Substitutionvalue of high-power root expression | 2 | 2 | Numerical valueCalculation | 2 | |
| Integer Roots Conditioninteger roots of quadratic from series expression | 2 | 2 | Numerical valueMulti-step | 1 | |
| Transformation of Rootsquadratic with transformed roots from given roots | 2 | 2 | Single correctMulti-step | – | |
| Roots in a Specific Ratioquadratic root ratio then conic latus rectum | 1 | 1 | Single correctMulti-step | – | |
| Vertex and Extrema Relationminimise parabola vertex distance from axis | 1 | 1 | Single correctMulti-step | – | |
| Range of Rational Quadratic Functionsrange of rational function then symmetric sum | 1 | 1 | Single correctMulti-step | – | |
| Always Negative Conditioncount parameter values for always-negative quadratic | 1 | 1 | Single correctApplication | – | |
| Zero Sum of Coefficients Shortcutstatement i/ii on quadratic roots and means | 1 | 1 | Two statementsMulti-step | – | |
| Quadratics with Absolute Valuessum of roots of modulus equation | 1 | 1 | Single correctMulti-step | – | |
| Difference of Rootsdifference of roots from ap and modulus conditions | 1 | 1 | Numerical valueMulti-step | 1 | |
| Reducible Biquadraticssum of modulus of non-real roots | 1 | 1 | Numerical valueMulti-step | 1 | |
| Resolution into Two Linear Factorsintegral parameter for real roots of reducible equation | 1 | 1 | Numerical valueMulti-step | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Quadratic Roots questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 202612 questions in 7 shifts
- 2 Apr, Shift 1Q1Let , be the roots of the quadratic equation…
Idea: Root-Coefficient Relation
Asked the year beforeHardSingle correct - 2 Apr, Shift 1Q23Let . If the probability, that for all , is ,…
Idea: Always Positive Condition
MediumNumerical value - 2 Apr, Shift 2Q1Let be the roots of the equation , and be the roots of the equation…
Idea: Symmetric Functions
Asked the year beforeMediumSingle correct - 2 Apr, Shift 2Q12Let the parabola passing through the point be such that the distance between its vertex and the -axis is…
Idea: Vertex and Extrema Relation
New ideaMediumSingle correct - 4 Apr, Shift 2Q2Let . Then is equal to:
Idea: Complex Conjugate Roots
EasySingle correct - 4 Apr, Shift 2Q4If and , where are two roots of the equation , , then…
Idea: Complex Conjugate Roots
MediumSingle correct - 5 Apr, Shift 1Q1Let . Let be the roots of the equation . If and…
Idea: Root-Coefficient Relation
Asked the year beforeMediumSingle correct - 5 Apr, Shift 2Q1Let be the roots of the equation and be the roots the equation ;…
Idea: Root-Coefficient Relation
Asked the year beforeMediumSingle correct - 5 Apr, Shift 2Q2Let be the distinct solutions of the equation . Then is equal to :
Idea: Root-Coefficient Relation
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q2Let one root of the quadratic equation in : be twice the other. Then the length of the latus rectum of…
Idea: Roots in a Specific Ratio
New ideaMediumSingle correct - 6 Apr, Shift 2Q2Consider the quadratic equation , . Let be the minimum value of the product of…
Idea: Root-Coefficient Relation
Asked the year beforeMediumSingle correct - 6 Apr, Shift 2Q3Let . Then is equal to :
Idea: Newton's Sums
Asked the year beforeMediumSingle correct
JEE Main 20256 questions in 5 shifts
- 2 Apr, Shift 1Q17Let , . If , , and , then the quadratic equation having roots…
Idea: Newton's Sums
Asked the year beforeMediumSingle correct - 3 Apr, Shift 1Q3Let and be the roots of , and and be the roots of . If…
Idea: Newton's Sums
Asked the year beforeMediumSingle correct - 3 Apr, Shift 1Q4Let be such that . Then the sum of all possible values of is
Idea: Symmetric Functions
Asked the year beforeMediumSingle correct - 3 Apr, Shift 2Q4Let the equation have equal roots. Then the distance of the point from the line…
Idea: Root-Coefficient Relation
Asked the year beforeEasySingle correct - 7 Apr, Shift 2Q2If the range of the function , , is , then is…
Idea: Range of Rational Quadratic Functions
New ideaMediumSingle correct - 8 Apr, Shift 2Q2The sum of the squares of the roots of and the squares of the roots of , is
Idea: Roots of Modulus Quadratics
Asked the year beforeMediumSingle correct
JEE Main 202420 questions in 16 shifts
- 4 Apr, Shift 1Q3If 2 and 6 are the roots of the equation , then the quadratic equation, whose roots are and…
Idea: Transformation of Roots
EasySingle correct - 4 Apr, Shift 2Q22Let . If …
Idea: Nature of Roots
HardNumerical value - 5 Apr, Shift 1Q22The number of distinct real roots of the equation is ________.
Idea: Roots of Modulus Quadratics
Asked the year beforeMediumNumerical value - 6 Apr, Shift 1Q4Let be the distinct roots of the equation , and . Then the…
Idea: Newton's Sums
Asked the year beforeHardSingle correct - 6 Apr, Shift 1Q21Let be the solution of the equation and…
Idea: Root-Coefficient Relation
Asked the year beforeHardNumerical value - 6 Apr, Shift 2Q21Let be roots of . If , then is equal to ________.
Idea: Newton's Sums
Asked the year beforeEasyNumerical value - 8 Apr, Shift 1Q3The sum of all the solutions of the equation is :
Idea: Exponential Reducible to Quadratic
EasySingle correct - 8 Apr, Shift 2Q21The number of distinct real roots of the equation , is ________
Idea: Roots of Modulus Quadratics
Asked the year beforeMediumNumerical value - 9 Apr, Shift 1Q2Let be the roots of the equation . The quadratic equation, whose roots are and…
Idea: Equation Formation
MediumSingle correct - 9 Apr, Shift 2Q3Let , be the roots of the equation . Let .…
Idea: Newton's Sums
Asked the year beforeMediumSingle correct - 1 Feb, Shift 1Q2Let . Then the number of elements in S is :
Idea: Exponential Reducible to Quadratic
MediumSingle correct - 1 Feb, Shift 2Q4Let and be the roots of the equation , where . If , and be the consecutive terms of a…
Idea: Root-Coefficient Relation
Asked the year beforeMediumSingle correct - 29 Jan, Shift 1Q21Let be the roots of the equation with . Then is…
Idea: Higher Degree Evaluation via Root Substitution
MediumNumerical value - 30 Jan, Shift 1Q22Let be roots of the equation , where . If …
Idea: Integer Roots Condition
MediumNumerical value - 30 Jan, Shift 2Q22The number of real solutions of the equation is ________.
Idea: Roots of Modulus Quadratics
Asked the year beforeMediumNumerical value - 31 Jan, Shift 1Q2Let S be the set of postive integral values of for which . Then, the…
Idea: Always Negative Condition
New ideaEasySingle correct - 31 Jan, Shift 1Q7Let be the sum of all coefficients in the expansion of and…
Idea: Complex Conjugate Roots
HardSingle correct - 31 Jan, Shift 1Q8For , let and be one of its root. Then, among the two statements (I) If…
Idea: Zero Sum of Coefficients Shortcut
New ideaMediumTwo statements - 31 Jan, Shift 2Q3Let and be two complex numbers such that and . Then, equals -
Idea: Symmetric Functions
HardSingle correct - 31 Jan, Shift 2Q24Let be the lengths of three sides of a triangle satisfying the condition . If the set of all…
Idea: Nature of Roots
HardNumerical value
JEE Main 20238 questions in 8 shifts
- 6 Apr, Shift 1Q2The sum of all the roots of the equation is:
Idea: Quadratics with Absolute Values
New ideaMediumSingle correct - 8 Apr, Shift 1Q3Let be the three roots of the equation . If , then…
Idea: Root-Coefficient Relation
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2 · Q22Roots of Modulus QuadraticsAsked the year beforeHard
- 11 Apr, Shift 1 · Q24Newton's SumsAsked the year beforeMedium
- 12 Apr, Shift 1 · Q2Newton's SumsAsked the year beforeHard
- 13 Apr, Shift 1 · Q2Roots of Modulus QuadraticsAsked the year beforeHard
- 13 Apr, Shift 2 · Q3Newton's SumsAsked the year beforeMedium
- 15 Apr, Shift 1 · Q2Roots of Modulus QuadraticsAsked the year beforeMedium
JEE Main 202221 questions in 19 shifts
- 25 Jul, Shift 2 · Q22Common Root ConditionAsked the year beforeHard
- 26 Jul, Shift 1 · Q21Common Root ConditionAsked the year beforeHard
- 26 Jul, Shift 2 · Q1Symmetric FunctionsAsked the year beforeEasy
- 28 Jul, Shift 1 · Q26Difference of RootsNew ideaMedium
- 28 Jul, Shift 1 · Q30Root-Coefficient RelationMedium
- 28 Jul, Shift 2 · Q62Transformation of RootsNew ideaMedium
- 29 Jul, Shift 2 · Q22Newton's SumsAsked the year beforeMedium
- 30 Jul, Shift 2 · Q81Roots of Modulus QuadraticsAsked the year beforeMedium
- 24 Jun, Shift 1 · Q7Symmetric FunctionsAsked the year beforeMedium
- 24 Jun, Shift 2 · Q2Exponential Reducible to QuadraticAsked the year beforeEasy
- 25 Jun, Shift 1 · Q26Higher Degree Evaluation via Root SubstitutionNew ideaMedium
- 25 Jun, Shift 2 · Q2Symmetric FunctionsAsked the year beforeMedium
- 26 Jun, Shift 1 · Q21Newton's SumsAsked the year beforeMedium
- 26 Jun, Shift 2 · Q22Symmetric FunctionsAsked the year beforeMedium
- 27 Jun, Shift 1 · Q22Exponential Reducible to QuadraticAsked the year beforeMedium
- 27 Jun, Shift 2 · Q22Symmetric FunctionsAsked the year beforeHard
- 28 Jun, Shift 1 · Q22Exponential Reducible to QuadraticAsked the year beforeHard
- 28 Jun, Shift 2 · Q2Root-Coefficient RelationMedium
- 29 Jun, Shift 1 · Q8Symmetric FunctionsAsked the year beforeMedium
- 30 Jun, Shift 1 · Q1Exponential Reducible to QuadraticAsked the year beforeMedium
- 30 Jun, Shift 1 · Q3Symmetric FunctionsAsked the year beforeMedium
JEE Main 202123 questions in 17 shifts
- 3 Aug, Shift 1 · Q82Reducible BiquadraticsNew ideaMedium
- 3 Aug, Shift 2 · Q62Common Root ConditionAsked the year beforeEasy
- 4 Aug, Shift 1 · Q61Exponential Reducible to QuadraticAsked the year beforeMedium
- 4 Aug, Shift 2 · Q82Resolution into Two Linear FactorsNew ideaHard
- 26 Aug, Shift 1 · Q83Nature of RootsAsked the year beforeMedium
- 26 Aug, Shift 2 · Q81Common Root ConditionAsked the year beforeMedium
- 27 Aug, Shift 1 · Q61Nature of RootsAsked the year beforeMedium
- 27 Aug, Shift 2 · Q62Nature of RootsAsked the year beforeHard
- 31 Aug, Shift 1 · Q62Exponential Reducible to QuadraticAsked the year beforeMedium
- 31 Aug, Shift 2 · Q63Exponential Reducible to QuadraticAsked the year beforeMedium
- 24 Feb, Shift 1 · Q62Symmetric FunctionsNew ideaMedium
- 24 Feb, Shift 1 · Q81Nature of RootsAsked the year beforeHard
- 24 Feb, Shift 2 · Q62Symmetric FunctionsNew ideaMedium
- 24 Feb, Shift 2 · Q90Roots of Modulus QuadraticsAsked the year beforeMedium
- 25 Feb, Shift 1 · Q63Always Positive ConditionNew ideaMedium
- 25 Feb, Shift 1 · Q76Nature of RootsAsked the year beforeMedium
- 25 Feb, Shift 2 · Q66Newton's SumsAsked the year beforeMedium
- 25 Feb, Shift 2 · Q69Complex Conjugate RootsAsked the year beforeEasy
- 26 Feb, Shift 2 · Q87Newton's SumsAsked the year beforeEasy
- 25 Jul, Shift 1 · Q72Exponential Reducible to QuadraticAsked the year beforeHard
- 25 Jul, Shift 1 · Q90Newton's SumsAsked the year beforeMedium
- 25 Jul, Shift 2 · Q74Roots of Modulus QuadraticsAsked the year beforeEasy
- 25 Jul, Shift 2 · Q84Newton's SumsAsked the year beforeMedium
JEE Main 202013 questions in 11 shifts
- 8 Jan, Shift 1 · Q52Complex Conjugate RootsNew ideaMedium
- 8 Jan, Shift 1 · Q71Nature of RootsNew ideaEasy
- 8 Jan, Shift 2 · Q53Roots of Modulus QuadraticsNew ideaMedium
- 9 Jan, Shift 1 · Q52Exponential Reducible to QuadraticNew ideaHard
- 9 Jan, Shift 2 · Q52Common Root ConditionNew ideaMedium
- 2 Sep, Shift 1 · Q52Newton's SumsNew ideaEasy
- 2 Sep, Shift 2 · Q52Equation FormationNew ideaMedium
- 3 Sep, Shift 1 · Q51Nature of RootsNew ideaMedium
- 3 Sep, Shift 1 · Q52Root-Coefficient RelationNew ideaMedium
- 4 Sep, Shift 1 · Q56Root-Coefficient RelationNew ideaMedium
- 4 Sep, Shift 2 · Q52Root-Coefficient RelationNew ideaMedium
- 5 Sep, Shift 1 · Q53Roots of Modulus QuadraticsNew ideaEasy
- 6 Sep, Shift 2 · Q52Root-Coefficient RelationNew ideaMedium
JEE Main 20171 question in 1 shift
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.