Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.1 NCERT Solutions
Neha Tanna6 May, 2026NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1 will help you understand how to recognise Quadratic Equations and express real-life situations in quadratic form. The exercise covers both identifying equations in standard form and converting word problems into mathematical expressions.
The step-by-step NCERT solutions make each concept easier to follow while improving accuracy and logical thinking. Based on the CBSE Class 10th syllabus, practicing these questions builds a strong foundation for solving quadratic equations in later exercises and enhances overall problem-solving confidence.
NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1
1. Check whether the following are quadratic equations:
(i) (x + 1) 2 = 2(x – 3)
(ii) x 2 – 2x = (–2) (3 – x)
(iii) (x – 2)(x + 1) = (x – 1)(x + 3)
(iv) (x – 3)(2x +1) = x(x + 5)
(v) (2x – 1)(x – 3) = (x + 5)(x – 1)
(vi) x 2 + 3x + 1 = (x – 2) 2
(vii) (x + 2) 3 = 2x (x 2 – 1)
(viii) x 3 – 4x 2 – x + 1 = (x – 2) 3
Solutions:
(i) Given, (x + 1) 2 = 2(x – 3) By using the formula for (a+b) 2 = a 2 +2ab+b 2 ⇒ x 2 + 2x + 1 = 2x – 6 ⇒ x 2 + 7 = 0 The above equation is in the form of ax 2 + bx + c = 0. Therefore, the given equation is quadratic.(iii) Given, (x – 2)(x + 1) = (x – 1)(x + 3) By multiplication ⇒ x2 – x – 2 = x 2 + 2x – 3 ⇒ 3x – 1 = 0 The above equation is not in the form of ax 2 + bx + c = 0. Therefore, the given equation is not quadratic.
(iv) Given, (x – 3)(2x +1) = x(x + 5) By multiplication ⇒ 2x2 – 5x – 3 = x 2 + 5x ⇒ x 2 – 10x – 3 = 0 The above equation is in the form of ax 2 + bx + c = 0. Therefore, the given equation is a quadratic equation.
(v) Given, (2x – 1)(x – 3) = (x + 5)(x – 1) By multiplication ⇒ 2x2 – 7x + 3 = x 2 + 4x – 5 ⇒ x 2 – 11x + 8 = 0 The above equation is in the form of ax 2 + bx + c = 0. Therefore, the given equation is a quadratic equation.
(vii) Given, (x + 2) 3 = 2x(x 2 – 1) By using the formula for (a+b) 3 = a 3 +b 3 +3ab(a+b) ⇒ x 3 + 8 + x 2 + 12x = 2x 3 – 2x ⇒ x 3 + 14x – 6x 2 – 8 = 0 The above equation is not in the form of ax 2 + bx + c = 0. Therefore, the given equation is not quadratic.
(viii) Given, x 3 – 4x 2 – x + 1 = (x – 2) 3 By using the formula for (a-b) 3 = a 3 -b 3 -3ab(a-b) ⇒ x 3 – 4x 2 – x + 1 = x 3 – 8 – 6x 2 + 12x ⇒ 2x 2 – 13x + 9 = 0 The above equation is in the form of ax 2 + bx + c = 0. Therefore, the given equation is quadratic.
2. Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m 2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken
Solutions:
(i) Let us consider, The breadth of the rectangular plot = x m Thus, the length of the plot = (2x + 1) m(ii) Let us consider, The first integer number = x Thus, the next consecutive positive integer will be = x + 1 Product of two consecutive integers = x × (x +1) = 306 ⇒ x 2 + x = 306 ⇒ x 2 + x – 306 = 0
Therefore, the two integers, x and x+1, satisfy the quadratic equation, x2 + x – 306 = 0, which is the required representation of the problem mathematically.
Therefore, the speed of the train satisfies the quadratic equation, x 2 – 8 x – 1280 = 0, which is the required representation of the problem mathematically.
NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1 PDF
Chapter 4 of Class 10 Maths, Quadratic Equations, introduces students to identifying and verifying quadratic expressions. Exercise 4.1 lays the foundation for understanding how quadratic equations are formed. To support easy learning, we’ve provided a detailed solution PDF with clear, step-by-step explanations. Check the Link given below;
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