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Mathematics - Quadratic Equation

Practise 199 JEE Main previous year questions on Quadratic Equation, compiled from papers spanning 2002 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Quadratic Equation has been asked in 24 of the 25 years of JEE Main papers analysed (2002–2026), with 199 questions in all. 24% of them were easy, 59% moderate and 17% tough. Most of its questions came from 2021, with 23 questions that year. In the last three years (2024–2026) it had 42 questions across 49 papers, about 0.9 per paper.

The chapter's 6 topics are not weighted equally: Relation between Roots and Coefficients (135 questions, 68%), N degree equation (25 questions, 13%), and Location of Roots (15 questions, 8%) have been asked the most. Relation between Roots and Coefficients has also led over the last five years, with 55 questions. Relation between Roots and Coefficients has produced the most tough questions (20).

  1. 1Let one root of the quadratic equation in : be twice the other. Then the length of the latus rectum of the parabola is equal to:06 Apr, 2026 (M)Relation between Roots and Coefficients
  2. 2Let and be two distinct roots of the equation . Let the sets , and . Then is equal to:06 Apr, 2026 (M)Location of Roots
  3. 3Consider the quadratic equation , . Let be the minimum value of the product of its roots and be the maximum value of the sum of its roots. T06 Apr, 2026 (E)Relation between Roots and Coefficients
  4. 4Let . Let be the roots of the equation . If and , then is equal to:05 Apr, 2026 (M)Relation between Roots and Coefficients
  5. 5Let , where , be the roots of the quadratic equation . Then is equal to:05 Apr, 2026 (M)Relation between Roots and Coefficients
  6. 6Let be the roots of the equation and be the roots the equation ; . If are in G.P., then equals :05 Apr, 2026 (E)Relation between Roots and Coefficients
  7. 7If and , where are two roots of the equation , , then is equal to:04 Apr, 2026 (E)Relation between Roots and Coefficients
  8. 8If the quadratic equation , , has two positive roots, then the number of possible integral values of is:04 Apr, 2026 (E)Location of Roots
  9. 9Let . If the probability, that for all , is , , then is equal to _______.02 Apr, 2026 (M)Graph and Sign of Quadratic
  10. 10Let be the roots of the equation , and be the roots of the equation . If the roots of the equation are and , then is equal to:02 Apr, 2026 (E)Relation between Roots and Coefficients
  11. 11Let and be a set of polynomials. Then the number of polynomials in S, which are divisible by , is28 Jan, 2026 (M)N degree equation
  12. 12If , where , are the roots of the equation such that , then the sum of all possible values of is28 Jan, 2026 (M)Relation between Roots and Coefficients
  13. 13The smallest positive integral value of , for which all the roots of are real and distinct, is equal to24 Jan, 2026 (E)N degree equation
  14. 14A 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 23 Jan, 2026 (M)N degree equation
  15. 15If and are the roots of the equation , then is equal to :23 Jan, 2026 (M)N degree equation
  16. 16The sum of all the real solutions of the equation is equal to23 Jan, 2026 (E)N degree equation
  17. 17Let be the roots of the quadratic equation . If , then the sum of all possible values of is :22 Jan, 2026 (E)Relation between Roots and Coefficients
  18. 18The sum of all the roots of the equation , is :21 Jan, 2026 (M)Relation between Roots and Coefficients
  19. 19Let and be the roots of the equation such that . Then the set of all possible values of is :21 Jan, 2026 (E)Location of Roots
  20. 20The sum of the squares of the roots of and the squares of the roots of , is08 Apr, 2025 (E)Relation between Roots and Coefficients
  21. 21Let the set of all values of , for which both the roots of the equation are negative real numbers, be the interval . Then is equal to07 Apr, 2025 (M)Relation between Roots and Coefficients
  22. 22For , let and be the roots of the equation If and , then is equal to ________.07 Apr, 2025 (E)Relation between Roots and Coefficients
  23. 23The number of real roots of the equation is :07 Apr, 2025 (E)Relation between Roots and Coefficients
  24. 24Consider the equation , where is a natural number. Then the number of all distinct values of , for which the given equation has integral roo04 Apr, 2025 (M)Relation between Roots and Coefficients
  25. 25Let and be the roots of , and and be the roots of . If and , then is equal to03 Apr, 2025 (M)Relation between Roots and Coefficients
  26. 26Let . If , and , then the quadratic equation having roots and is :02 Apr, 2025 (M)Relation between Roots and Coefficients
  27. 27If the set of all , for which the roots of the equation are positive is , then is equal to _______ .02 Apr, 2025 (E)Relation between Roots and Coefficients
  28. 28The number of solutions of the equation \( ( {9}{x}- {9}{ {x}}+2 ) ( {2}{x}- {7}{ {x}}+3 )=0\) is:29 Jan, 2025 (M)N degree equation
  29. 29If the set of all , for which the equation has no real root, is the interval , and , then is equal to :29 Jan, 2025 (E)Relation between Roots and Coefficients
  30. 30The sum, of the squares of all the roots of the equation , is28 Jan, 2025 (M)Relation between Roots and Coefficients
  31. 31The product of all the rational roots of the equation , is equal to24 Jan, 2025 (M)N degree equation
  32. 32If the equation has equal roots, where and , then is equal to23 Jan, 2025 (M)Common Roots
  33. 33Let and be the distinct roots of . If m and M are the minimum and the maximum values of , then equals :22 Jan, 2025 (E)Relation between Roots and Coefficients
  34. 34Let be the roots of the equation . The quadratic equation, whose roots are and , is :09 Apr, 2024 (M)Relation between Roots and Coefficients
  35. 35Let , be the roots of the equation . Let . Then is equal to09 Apr, 2024 (E)Relation between Roots and Coefficients
  36. 36The sum of all the solutions of the equation is :08 Apr, 2024 (M)Relation between Roots and Coefficients
  37. 37The number of distinct real roots of the equation , is08 Apr, 2024 (E)Location of Roots
  38. 38Let be the distinct roots of the equation and . Then the minimum value of is06 Apr, 2024 (M)Relation between Roots and Coefficients
  39. 39Let be the solution of the equation and . Then the value of is06 Apr, 2024 (M)N degree equation
  40. 40Let be roots of . If , then is equal to______06 Apr, 2024 (E)Relation between Roots and Coefficients
  41. 41The number of real solutions of the equation is_________05 Apr, 2024 (E)Relation between Roots and Coefficients
  42. 42If 2 and 6 are the roots of the equation , then the quadratic equation, whose roots are and , is :04 Apr, 2024 (M)Relation between Roots and Coefficients
  43. 43Let S = x ∈ R : 3 + 2 x + 3 − 2 x = 10 . Then the number of elements in S is:01 Feb, 2024 (M)N degree equation
  44. 44Let α and β be the roots of the equation p x 2 + q x − r = 0 , where p ≠ 0 . If p , q and r be the consecutive terms of a non-constant G.P a01 Feb, 2024 (E)Relation between Roots and Coefficients
  45. 45Let S be the set of positive integral values of a for which a x 2 + 2 a + 1 x + 9 a + 4 x 2 - 8 x + 32 0 , ∀ x ∈ ℝ . Then, the number of ele31 Jan, 2024 (M)Graph and Sign of Quadratic
  46. 46For 0 c b a , let ( a + b – 2 c ) x 2 + ( b + c – 2 a ) x + ( c + a – 2 b ) = 0 and α ≠ 1 be one of its root. Then, among the two statements31 Jan, 2024 (M)Relation between Roots and Coefficients
  47. 47Let a , b , c be the length of three sides of a triangle satisfying the condition a 2 + b 2 x 2 − 2 b a + c x + b 2 + c 2 = 0 . If the set o31 Jan, 2024 (E)Relation between Roots and Coefficients
  48. 48The number of solutions, of the equation e sin x − 2 e − sin x = 2 is31 Jan, 2024 (E)N degree equation
  49. 49Let \( , \) be roots of equation \(x^2-70 x+ =0\), where \( { }{2}, { }{3} \). If \( \) assumes the minimum possible value, then \( {( { -1}30 Jan, 2024 (M)Relation between Roots and Coefficients
  50. 50The number of real solutions of the equation \(x (x^2+3|x|+5|x-1|+6|x-2| )=0\) is ______.30 Jan, 2024 (E)N degree equation

Frequently Asked Questions

1.How many questions are available for Quadratic Equation?

This chapter includes 199 questions compiled from JEE Main papers spanning 2002 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Quadratic Equation chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Quadratic Equation an important chapter for JEE Main Mathematics?

Quadratic Equation has appeared in 24 of the 25 years of JEE Main papers covered here, with 199 questions across 164 papers - about one per paper it appears in.

4.What is the difficulty level of Quadratic Equation questions in JEE Main?

Of the 199 questions analysed for this chapter, 24% are easy, 59% moderate and 17% tough. 2021 had the most, with 23 questions.

5.Which topics in Quadratic Equation should I focus on?

These topics have carried the most weightage in Quadratic Equation:

  • Relation between Roots and Coefficients - 135 questions (68%)
  • N degree equation - 25 questions (13%)
  • Location of Roots - 15 questions (8%)
  • Relation between Roots and Coefficients has produced the most tough questions (20).
6.Is Quadratic Equation's weightage in JEE Main going up or down?

Across all 164 papers analysed, Quadratic Equation has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.9 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.