CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus
NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations
Try each question first: pick an option or type your final answer, then see the full step-by-step solution. Stuck? Open the first step as a hint. Free, no account needed.
Boards begin February 2027
Pre-boards are in December
Quadratic Equations is in Algebra, which carries 20 of the 80 marks in the 2026-27 CBSE Maths paper
14 NCERT textbook questions from Chapter 4
Exercise 4.1
NCERT Ex 4.1 Q1(iii)2 marks
Check whether (x − 2)(x + 1) = (x − 1)(x + 3) is a quadratic equation.
Step 1LHS: (x − 2)(x + 1) = x² − x − 2.
Step-by-step solution
LHS: (x − 2)(x + 1) = x² − x − 2.
RHS: (x − 1)(x + 3) = x² + 2x − 3.
Set LHS = RHS: x² − x − 2 = x² + 2x − 3 ⇒ −3x + 1 = 0 (the x² terms cancel).
The equation is linear (degree 1), NOT of the form ax² + bx + c = 0 with a ≠ 0. Hence it is not a quadratic equation.
Answer:Not a quadratic equation (the x² terms cancel; result is linear).
CBSE board pattern: Assertion-Reason and case-based questions
Written in the CBSE board format. These are not numbered NCERT/Exemplar questions; some case studies are built on textbook problems. Neither NCERT book has Assertion-Reason questions: they, and case-based questions, are a CBSE board-paper format, here on this chapter's 2026-27 syllabus, with solutions by LazyTopper.
CBSE board pattern · Assertion-Reason1 mark
Assertion (A): The quadratic equation 2x² − 6x + 3 = 0 has two distinct real roots.
Reason (R): A quadratic equation ax² + bx + c = 0 has two distinct real roots if and only if b² − 4ac > 0.
Step 1Check Assertion: 2x² − 6x + 3 = 0 → a = 2, b = −6, c = 3 → D = 36 − 24 = 12 > 0 → two distinct real roots. Assertion is TRUE.
Step-by-step solution
Check Assertion: 2x² − 6x + 3 = 0 → a = 2, b = −6, c = 3 → D = 36 − 24 = 12 > 0 → two distinct real roots. Assertion is TRUE.
Check Reason: The standard discriminant test states D > 0 ⇔ two distinct real roots. Reason is TRUE.
Reason directly explains why Assertion holds (we used D > 0 to conclude distinct roots).
Hence option (A).
Answer:Option (A) — both true and Reason explains Assertion.
A charity trust is constructing a rectangular prayer hall with carpet area 300 m². The length of the hall is one metre more than twice its breadth.
(i) If the breadth is x m, write a quadratic equation in x for the carpet area.
(ii) Factorise the equation to find the breadth and the length of the hall.
Step 1(i) Breadth = x m ⇒ length = (2x + 1) m. Area = length × breadth = x(2x + 1) = 2x² + x = 300, so 2x² + x − 300 = 0.
Step-by-step solution
(i) Breadth = x m ⇒ length = (2x + 1) m. Area = length × breadth = x(2x + 1) = 2x² + x = 300, so 2x² + x − 300 = 0.
A cottage industry produces a certain number of pottery articles in a day. On a particular day, the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day, and the total cost of production that day was ₹90.
(i) If x articles were produced, set up the quadratic equation in x.
(ii) Solve to find the number of articles and the cost of each article.
Step 1(i) Number of articles = x. Cost per article (in ₹) = 2x + 3. Total cost = x(2x + 3) = 90 ⇒ 2x² + 3x − 90 = 0.
Step-by-step solution
(i) Number of articles = x. Cost per article (in ₹) = 2x + 3. Total cost = x(2x + 3) = 90 ⇒ 2x² + 3x − 90 = 0.
Board examiners mark every step. Photograph your written answer and see the marks for each step, and exactly where they were lost. Your first answer check is free.
Questions from the NCERT Class 10 Mathematics textbook (the CBSE board-pattern section is in the board format, not numbered book questions); the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.