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Mathematics - Quadratic Equation

Practise 82 NTA Abhyas (JEE Main) questions on Quadratic Equation. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Quadratic Equation has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 82 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1If a + b + c 9 c 4 and the equation a x 2 + 2 b x - 5 c = 0 has non-real complex roots, then
  2. 2The number of roots of the equation 2 2 x + 1 = 2 x - 1 is equal to
  3. 3If p , q , r , s ∈ R, then the equation x 2 + p x + 3 q - x 2 + r x + q - x 2 + s x - 2 q = 0 has
  4. 4If a 2 , then the roots of the equation 2 - a x 2 + 3 a x - 1 = 0 are
  5. 5If , are the roots of the equation x 2 3 x + 4 = 0 , then the equation whose roots are - 2 + 2 , - 2 + 2 is
  6. 6The number of natural numbers n for which the equation x - 8 x = n n - 10 has no real solution is equal to
  7. 7If a , b , c are real numbers satisfying the condition a + b + c = 0, then the roots of the quadratic equation 3 a x 2 + 5 b x + 7 c = 0 are
  8. 8If and are the roots of the equation x 2 + x + = 0 such that , then the number of integral values of x satisfying x - - 1 is
  9. 9If α is a root of the equation 4 x 2 + 2 x - 1 = 0 and f x = 4 x 3 - 3 x + 1, then 2 f α + α is equal to
  10. 10The smallest possible natural number n , for which the equation x 2 - n x + 2014 = 0 has integral roots, is
  11. 11Let f x = x 2 + 2 p x + 2 q 2 and g x = - x 2 - 2 q x + p 2 (where q 0 ). If x R and the the minimum value of f x is equal to the maximum va
  12. 12Let two numbers have an arithmetic mean 9 and geometric mean 4 , then these numbers are the roots of the quadratic equation
  13. 13If the equations 2 x 2 - 7 x + 9 = 0 and a x 2 + b x + 18 = 0 have a common root, then a , b ∈ R
  14. 14If but, 2 = 4 - 2 and 2 = 4 - 2 , then the quadratic equation with roots and is
  15. 15If α , β and γ are the roots of the equation x 3 - 13 x 2 + 15 x + 189 = 0 and one root exceeds the other by 2, then the value of α + β + γ
  16. 16The quadratic equation whose roots are the arithmetic mean and the harmonic mean of the roots of the equation x 2 + 7 x - 1 = 0 is
  17. 17The line K + 1 2 x + Ky - 2 K 2 - 2 = 0 passes through the point m , n for all real values of K , then
  18. 18If α and β are the roots of the equation 2 x 2 + 4 x - 5 = 0 , then the equation whose roots are 1 2 α - 3 and 1 2 β - 3 is
  19. 19If α and β are the roots of the equation 8 x 2 - 3 x + 27 = 0 , then the value of α 2 β 1 3 + β 2 α 1 3 is
  20. 20The quadratic equation 1 - sin ⁡ θ x 2 + 2 1 - sin ⁡ θ x - 3 sin ⁡ θ = 0 has both roots complex for all θ lying in the interval
  21. 21The set of all the possible real values of a such that the inequality x - a - 1 x - a 2 + 2 0 holds for all x - 1 , 3 , is
  22. 22If both the roots of the equation x 2 + a - 1 x + a = 0 are positive, then the complete solution set of real values of a is
  23. 23If the roots of the equation a x 2 + b x + c = 0 are in the ratio m : n , then
  24. 24For real x , the function ( x - a ) ( x - b ) ( x - c ) will assume all real values provided
  25. 25Let A be the set of values of k for which 2 lies between the roots of the quadratic equation x 2 + k + 2 x - k + 3 = 0 , then A is given by
  26. 26If the roots of the equation x 3 + b x 2 + c x + d = 0 are in arithmetic progression, then b , c and d satisfy the relation
  27. 27The quadratic equations x 2 - 6 x + a = 0 and x 2 - c x + 6 = 0 have one root in common. The other roots of the first equation and the secon
  28. 28If both the roots of the equation x 2 - m x + 1 = 0 are less than unity, then
  29. 29Let P x = x 2 + bx + c , where b and c are integers. If P ( x ) is a factor of both x 4 + 6 x 2 + 2 5 and 3 x 4 + 4 x 2 + 2 8 x + 5 , then t
  30. 30The possible values of n for which the equation n x 2 + 2 n – 1 x + n – 1 = 0 has roots of opposite sign is/are given by
  31. 31Let α and β be the roots of the equation x 2 + ax + 1 = 0 , a ≠ 0 . Then the equation whose roots are - α + 1 β and - 1 α + β is
  32. 32The sum of all real values of x satisfying the equation x 2 - 5 x + 5 x 2 + 4 x - 60 = 1 is
  33. 33Set of all the values of x satisfying the inequality x 2 - 7 x + 6 x + 2 is
  34. 34The range of a for which the equation x 2 + a x - 4 = 0 has its smaller root in the interval - 1 , 2 is
  35. 35If α and β are the roots of the equation x 2 + x + c = 0 such that α + β , α 2 + β 2 and α 3 + β 3 are in arithmetic progression, then c is
  36. 36If the equation a x 2 + 2 b x - 3 c = 0 has no real roots and 3 c 4 a + b , then
  37. 37Let α and β are the roots of equation a x 2 + b x + c = 0 a ≠ 0 . If 1 , α + β , α β are in arithmetic progression and α , 2 , β are in harm
  38. 38If α , β and γ are the roots of the equation x 3 - p x 2 + q x - r = 0 , then the value of α β γ + β γ α + γ α β is equal to
  39. 39If both the roots of the equation 4 x 2 - 2 x + m = 0 lie in the interval - 1,1 , then
  40. 40If α and β are the roots of 4 x 2 - 16 x + t = 0 , ∀ t 0 such that 1 α 2 β 3 , then the number of integral values of t are
  41. 41If x is rational and 4 x 2 + 1 x 2 + 1 6 x + 1 x - 5 7 = 0 , ⁡ then the product of all possible values of x is
  42. 42The number of quadratic equations that are unchanged by squaring their roots is
  43. 43Let , and be the roots of the equation x 3 + x + 1 = 0 , then + + + + + 2 + 2 + 2 is equal to
  44. 44For the equation x 2 - 2 x - 3 = b , which of the following statements is true?
  45. 45If one root of the equation x 2 + p x + q = 0 is the square of the other, then
  46. 46If both roots of x 2 - 2 a x + a 2 + a - 3 = 0 are less than 3 , then
  47. 47If the graph of the function y = a - b 2 x 2 + 2 a + b - 2 c x + 1 a b is strictly above the x -axis, then
  48. 48The value of k for which both the roots of the equation 4 x 2 - 20 k x + 25 k 2 + 15 k - 66 = 0 are less than 2 , lies in
  49. 49If f x = a x 2 + b x + c , f - 1 1 2 , f 1 - 1 and f - 3 - 1 2 , then
  50. 50The number of real solutions of the equation x + 14 - 8 x - 2 + x + 23 - 10 x - 2 = 3 are

Frequently Asked Questions

1.How many questions are available for Quadratic Equation?

This chapter includes 82 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Quadratic Equation questions in NTA Abhyas (JEE Main)?

Of the 82 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.