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Mathematics - Quadratic Equation

Practise 19 JEE Advanced previous year questions on Quadratic Equation, compiled from papers spanning 2006 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 Advanced tests.

Quadratic Equation has been asked in 16 of the 27 years of JEE Advanced papers analysed (2000–2026), with 19 questions in all. 16% of them were easy, 53% moderate and 32% tough. Most of its questions came from 2026, with 2 questions that year. In the last three years (2024–2026) it had 3 questions across 6 papers, about 0.5 per paper.

The chapter's 4 topics are not weighted equally: Relation between Roots and Coefficients (16 questions, 84%), Common Roots (1 question, 5%), and Descartes Rule of Sign (1 question, 5%) have been asked the most. Relation between Roots and Coefficients has also led over the last five years, with 3 questions. Relation between Roots and Coefficients has produced the most tough questions (5).

  1. 1Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) If and are the distinct roots o2026 (Paper 1)Relation between Roots and Coefficients
  2. 2Let be positive integers in arithmetic progression such that the equation has only integer solutions. Then which of the following statements2026 (Paper 2)Relation between Roots and Coefficients
  3. 3Let be a polynomial with real coefficients such that . Suppose that is a root of the equation , where . If , and are all the roots of the eq2024 (Paper 1)Relation between Roots and Coefficients
  4. 4For x R , the number of real roots of the equation 3 x 2 - 4 x 2 - 1 + x - 1 = 0 is2021 (Paper 1)N degree equation
  5. 5Suppose a , b denote the distinct real roots of the quadratic polynomial x 2 + 20 x 2020 and suppose c , d denote the distinct complex roots2020 (Paper 1)Relation between Roots and Coefficients
  6. 6Let and be the roots of x 2 - x - 1 = 0 , with . For all positive integers n , define a n = n - n - , n 1 b 1 = 1 and b n = a n - 1 + a n + 2019 (Paper 1)Relation between Roots and Coefficients
  7. 7Paragraph: Let be integers and let be the roots of the equation, , where . For , let FACT: If and are rational numbers and , then . Question2017 (Paper 2)Relation between Roots and Coefficients
  8. 8Paragraph: Let be integers and let be the roots of the equation, , where . For , let FACT: If and are rational numbers and , then . Question2017 (Paper 2)Relation between Roots and Coefficients
  9. 9Let - 6 - 12 . Suppose 1 and 1 are the roots of the equation x 2 - 2 x sec + 1 = 0 and 2 and 2 are the roots of the equation x 2 + 2 x tan -2016 (Paper 1)Relation between Roots and Coefficients
  10. 10Let S be the set of all non - zero real numbers such that the quadratic equation x 2 - x + = 0 has two distinct real roots x 1 a n d x 2 sat2015 (Paper 2)Relation between Roots and Coefficients
  11. 11The quadratic equation p ( x ) = 0 with real coefficients has purely imaginary roots. Then the equation p ( p ( x ) ) = 0 has2014 (Paper 2)Relation between Roots and Coefficients
  12. 12The value of2012 (Paper 1)Descartes Rule of Sign
  13. 13Let and be the roots of with . If for , then the value of is2011 (Paper 1)Relation between Roots and Coefficients
  14. 14The value of for which the equations have one root in common is2011 (Paper 2)Common Roots
  15. 15Let and be real numbers such that and . If and are non-zero complex numbers satisfying and , then quadratic equation having and as its roots2010 (Paper 1)Relation between Roots and Coefficients
  16. 16The smallest value of , for which both the roots of the equation are real, distinct and have values atleast 4 , is2009 (Paper 2)Relation between Roots and Coefficients
  17. 17Let be real numbers. Suppose, are the roots of the equation and are the roots of the equation , where . Statement . Statement or .2008 (Paper 2)Relation between Roots and Coefficients
  18. 18Let be the roots of the equation and be the roots of the equation . Then, the value of is2007 (Paper 1)Relation between Roots and Coefficients
  19. 19If have roots and and have roots and , then, find .2006Relation between Roots and Coefficients

Frequently Asked Questions

1.How many questions are available for Quadratic Equation?

This chapter includes 19 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

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

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

Quadratic Equation has appeared in 16 of the 21 years of JEE Advanced papers covered here, with 19 questions across 18 papers - about one per paper it appears in.

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

Of the 19 questions analysed for this chapter, 16% are easy, 53% moderate and 32% tough. 2026 had the most, with 2 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 - 16 questions (84%)
  • Common Roots - 1 question (5%)
  • Descartes Rule of Sign - 1 question (5%)
  • Relation between Roots and Coefficients has produced the most tough questions (5).
6.Is Quadratic Equation's weightage in JEE Advanced going up or down?

Across all 18 papers analysed, Quadratic Equation has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.5 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.