CBSE Class 10 Mathematics (Basic) Chapter 4 Quadratic Equations Important Questions 2027
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27 questions from Quadratic Equations appeared in 7 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Algebra unit — 20 marks in the official syllabus
- Asked in 7 of 7 analysed papers (2022–2026)
- About 3.9 questions per paper (OR alternatives counted separately)
- 6 question patterns repeated across papers
Important topics in Quadratic Equations
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Word problems on quadratic equations | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 2 | Nature of roots / discriminant | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Checking whether an equation is quadratic / standard form | Board 2022Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| 4 | Solving by quadratic formula | Board 2022 | ★☆☆☆☆ |
Repeated questions from Quadratic Equations
1. Determine nature of roots
3×Board 2022Sample 2025Sample 20261/2 marks
Find the nature of roots of the quadratic equation x2 + 4x − 3√2 = 0.
2. Train speed-distance-time
2×Sample 2025Sample 20265 marks
A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hr, it takes 2 hours less in the journey. Find the original speed of the train.
3. Find k for equal roots
3×Board 2024Board 2025Board 20261/5 marks
Find the value(s) of k for which the equation 2x2 + kx + 3 = 0 has real and equal roots. Hence, find the roots of the equations so obtained.
4. Find the discriminant
3×Board 2023Board 2025Board 20261 marks
The discriminant of the quadratic equation x2 – 3x – 2 = 0 is : (A) 1 (B) 17 (C) √17 (D) – √17
5. Reduce rational eqn, find a-b+c
2×Board 2025Board 20261 marks
The equation x + 1/x = 3 (x ≠ 0) is expressed as a quadratic equation in the form of ax2 + bx + c = 0. The value of a – b + c is : (A) 5 (B) 2 (C) 1 (D) – 1
6. Difference-of-squares numbers
2×Board 2025Board 20265 marks
The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.
Quadratic Equations questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 3 | 6 |
| Board 2023 | 3 | 11 |
| Board 2024 | 5 | 7 |
| Board 2025 | 4 | 12 |
| Sample 2025 | 4 | 12 |
| Board 2026 | 4 | 12 |
| Sample 2026 | 4 | 13 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Quadratic Equations
Board 2026 4 questions
The discriminant of the quadratic equation x2 – 3x – 2 = 0 is : (A) 1 (B) 17 (C) √17 (D) – √17
The equation x + 1/x = 3 (x ≠ 0) is expressed as a quadratic equation in the form of ax2 + bx + c = 0. The value of a – b + c is : (A) 5 (B) 2 (C) 1 (D) – 1
The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.
Find the value(s) of k for which the equation 2x2 + kx + 3 = 0 has real and equal roots. Hence, find the roots of the equations so obtained.
Sample 2026 4 questions
Which of the following is not a quadratic equation?
A) (x + 2)2 = 2(x + 3)
B) x2 + 3x = (−1)(1 − 3x2)
C) (x + 2)(x − 1) = x2 − 2x − 3
D) x3 − x2 + 2x + 1 = (x + 1)3
Find the nature of roots of the quadratic equation x2 + 4x − 3√2 = 0.
The numerator of a fraction is 3 less than its denominator. If 2 is added to both of its numerator and denominator then the sum of the new fraction and original fraction is 29/20. Find the original fraction.
A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hr, it takes 2 hours less in the journey. Find the original speed of the train.
Board 2025 4 questions
The discriminant of the quadratic equation x2 - 3x - 2 = 0 is : (A) 1 (B) 17 (C) √17 (D) -√17
The equation x + 1/x = 3 (x ≠ 0) is expressed as a quadratic equation in the form of ax2 + bx + c = 0. The value of a - b + c is : (A) 5 (B) 2 (C) 1 (D) -1
The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.
Find the value(s) of k for which the equation 2x2 + kx + 3 = 0 has real and equal roots. Hence, find the roots of the equations so obtained.
Sample 2025 4 questions
The value of k for which the quadratic equation kx2 − 5x + 1 = 0 does not have a real solution, is (A) 0 (B) 25/4 (C) 4/25 (D) 7
The roots of quadratic equation 3x2 − 4√3x + 4 = 0 are (A) not real (B) real and equal (C) rational and distinct (D) irrational and distinct
Amita buys some books for ₹1920. If she had bought 4 more books for the same amount each book would cost her ₹24 less. How many books did she buy? What was the initial price of one book?
A train travels at a certain average speed for a distance of 132 km and then travels a distance of 140 km at an average speed of 4 km/h more than the initial speed. If it takes 4 hours to complete the whole journey, what was the initial average speed? Determine the time taken by train to cover the distances separately.
Board 2024 5 questions
If the roots of quadratic equation 4x2 - 5x + k = 0 are real and equal, then value of k is : (a) 5/4 (b) 25/16 (c) -5/4 (d) -25/16
[Case: Two sprinkler circles touch externally; the sum of their areas is 130π sq m and the distance between their centres is 14 m.] Obtain a quadratic equation involving R and r from above.
[Case: Two sprinkler circles touch externally; the sum of their areas is 130π sq m and the distance between their centres is 14 m.] Write a quadratic equation involving only r.
[Case: Two sprinkler circles touch externally; the sum of their areas is 130π sq m and the distance between their centres is 14 m.] Find the radius r and the corresponding area irrigated.
[Case: Two sprinkler circles touch externally; the sum of their areas is 130π sq m and the distance between their centres is 14 m.] Find the radius R and the corresponding area irrigated.
Board 2023 3 questions
The discriminant of the quadratic equation 2x2 − 5x − 3 = 0 is : (a) 1 (b) 49 (c) 7 (d) 19
The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 80 m more than the shorter side, find the length of the sides of the field.
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present age.
Board 2022 3 questions
Find the nature of the roots of the quadratic equation x2 - 5x + 9 = 0.
Write a quadratic equation with roots -3 and 5.
Solve the quadratic equation 2x2 - 5x - 1 = 0 for x.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 4 Quadratic Equations?
By how often and how recently they were asked: Word problems on quadratic equations; Nature of roots / discriminant; Checking whether an equation is quadratic / standard form.
How many marks does Quadratic Equations carry in the CBSE Class 10 Mathematics (Basic) exam?
Quadratic Equations is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 3.9 questions per paper.
Do questions from Quadratic Equations repeat in board exams?
Yes — 6 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.