Class 10 Maths Ch4 Quadratic Equations – NCERT Solutions, exercise by exercise. Pick an exercise:
Exercise 4.1
Exercise 4.2
Exercise 4.3
About NCERT Class 10 Maths Chapter 4
Quadratic Equations is Chapter 4 of the NCERT Class 10 Mathematics textbook. It builds on quadratic polynomials and shows how equations of degree two arise in geometry, number problems, speed-and-time questions, ages, area, and other everyday situations. The exercise sequence and topic coverage on this page have been checked against the NCERT Mathematics textbook, Chapter 4, Reprint 2026-27.
What is a quadratic equation?
A quadratic equation in the variable x has the standard form ax^2 + bx + c = 0, where a, b and c are real numbers and a is not equal to 0. Before deciding whether an equation is quadratic, simplify both sides and arrange all terms on one side. An equation that initially looks cubic may reduce to a quadratic equation, while apparent squared terms may cancel and leave a linear equation.
A real number r is a root of ax^2 + bx + c = 0 when ar^2 + br + c = 0. The roots of the equation are the same as the zeroes of the corresponding quadratic polynomial. A quadratic equation can have at most two real roots.
Methods and ideas covered
– Forming a quadratic equation from a word problem.
– Checking an equation after simplification and writing it in standard form.
– Finding roots by factorisation, usually by splitting the middle term and equating each linear factor to zero.
– Using the quadratic formula when real roots exist.
– Using the discriminant to decide the nature of the roots before solving.
– Rejecting a mathematically valid root when it is not meaningful in the given situation, such as a negative length or distance.
Key formulas and facts
Standard form: ax^2 + bx + c = 0, where a is not equal to 0.
Quadratic formula: x = [-b +/- sqrt(b^2 – 4ac)] / (2a), provided b^2 – 4ac is greater than or equal to 0.
Discriminant: D = b^2 – 4ac.
– If D > 0, the equation has two distinct real roots.
– If D = 0, the equation has two equal real roots, each equal to -b / (2a).
– If D < 0, the equation has no real roots.
Exercise-wise coverage
Exercise 4.1 focuses on recognising quadratic equations after simplification and translating situations involving areas, consecutive integers, ages, and travel into quadratic equations.
Exercise 4.2 develops the factorisation method. It includes direct root-finding questions and applications involving numbers, a right triangle, and production costs.
Exercise 4.3 uses the discriminant to identify the nature of roots, find conditions for equal roots, and test whether real-life designs or age situations are possible.
How to use these NCERT solutions
1. Write the equation in standard form and identify a, b and c with their signs.
2. Try each exercise independently before opening the solution.
3. Compare every transformation, not just the final answer.
4. Substitute the roots into the original equation to verify them.
5. In word problems, check units and discard answers that do not fit the context.
Quick revision questions
What is the degree of a quadratic equation?
The highest power of the variable is 2 after the equation is simplified.
How many real roots can a quadratic equation have?
It can have two distinct real roots, two equal real roots, or no real roots.
What does the discriminant tell us?
The sign of b^2 – 4ac tells us the nature of the roots without first calculating both roots.
Which exercise should I start with?
Start with Exercise 4.1 to practise forming equations, continue to Exercise 4.2 for factorisation, and finish with Exercise 4.3 for the discriminant and nature of roots.
Source note
This overview follows NCERT Class 10 Mathematics, Chapter 4: Quadratic Equations, Reprint 2026-27. The explanations are independently written for LearnCBSE.net and are organised to help students move from the textbook concepts to the exercise solutions.