---
source: ncert_exercises
topic: algebra
class_level: class_10
chapter: ch4
exercise: ex4.1
difficulty: intermediate
---

Class 10 | Ch4: Quadratic Equations | Exercise 4.1

Standard form: ax² + bx + c = 0, where a ≠ 0.
A quadratic equation has at most 2 roots.

Q1. Check whether the following are quadratic equations:
(i) (x+1)²=2(x-3)  (ii) x²-2x=(-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) x²+3x+1=(x-2)²
(vii) (x+2)³=2x(x²-1)  (viii) x³-4x²-x+1=(x-2)³
Answer:
(i) x²+2x+1=2x-6 → x²+8=0. YES, quadratic (a=1,b=0,c=8). ✅
(ii) x²-2x=-6+2x → x²-4x+6=0. YES. ✅
(iii) x²-x-2=x²+2x-3 → -3x+1=0 → 3x=1. NO, linear. ✅
(iv) 2x²-5x-3=x²+5x → x²-10x-3=0. YES. ✅
(v) 2x²-7x+3=x²+4x-5 → x²-11x+8=0. YES. ✅
(vi) x²+3x+1=x²-4x+4 → 7x-3=0. NO, linear. ✅
(vii) x³+6x²+12x+8=2x³-2x → x³-6x²-14x-8=0. NO, cubic. ✅
(viii) x³-4x²-x+1=x³-6x²+12x-8 → 2x²-13x+9=0. YES. ✅

Q2. Represent the following as quadratic equations:
(i) Area of rectangular plot=528 m², length is 1 more than twice the breadth.
(ii) Product of two consecutive positive integers is 306.
(iii) Rohan's mother is 26 years older. Product of ages 3 years from now = 360.
(iv) Express train takes 1hr less than passenger train for 132 km. Express speed is 11 km/h more.
Answer:
(i) Let breadth=x. Length=2x+1. x(2x+1)=528 → 2x²+x-528=0. ✅
(ii) x(x+1)=306 → x²+x-306=0. ✅
(iii) Let Rohan's age=x. Mother=x+26. (x+3)(x+29)=360 → x²+32x+87=360 → x²+32x-273=0. ✅
(iv) Let passenger speed=x. Express=x+11. 132/x-132/(x+11)=1 → x²+11x-1452=0. ✅