NCERT Exemplar Solutions for Class 10 Maths Chapter 4 Quadrilateral Equations Exercise 4.3

Chapter 4 Quadrilateral Equations NCERT Exemplar Solutions Exercise 4.3 Class 10 Maths

Chapter Name	NCERT Maths Exemplar Solutions for Chapter 4 Quadrilateral Equations Exercise 4.3
Book Name	NCERT Exemplar for Class 10 Maths
Other Exercises	Exercise 4.1 Exercise 4.2 Exercise 4.4
Related Study	NCERT Solutions for Class 10 Maths

Exercise 4.3 Solutions

1. Find the roots of the quadratic equations by using the quadratic formula in each of the following.
(i) 2x² - 3x - 5 = 0 
(ii) 5x² + 13x + 8 = 0 
(iii) -3x² + 5x + 12 = 0 
(iv) -x² + 7x - 10 = 0 
(v) x² + 2√2x - 6 = 0 
(vi) x² - 3√5x + 10 = 0 
(vii) (1/2)x² - √11x + 1 = 0 

Solution
The quadratic formula to find the roots of quadratic equation ax² + bx + c = 0, a ≠ 0 is given by, 

2. Find the roots of the following quadratic equations by the factorization method : 

(i) 2x² + (5/3)x - 2 = 0
(ii) (2/5)x² - x - 3/5 = 0
(iii) 3√2 x² - 5x - √2 = 0
(iv) 3x² + 5√5x - 10 = 0
(v) 21x² - 2x + 1/21 = 0
Solution

(i) 2x² + (5/3)x - 2 = 0 
⇒ 6x² + 5x - 6 = 0 
⇒ 6x² + 9x - 4x - 6 = 0 
⇒ 3x(2x + 3)-2(2x + 3) = 0 
⇒ (2x + 3)(3x - 2) = 0 
⇒ 2x + 3  = 0 or 3x - 2 = 0 
⇒ 2x = -3 or 3x = 2 
So, the roots of the given quadratic equation are -3/2 and 2/3.

(ii) (2/5)x² - x - 3/5 = 0 
⇒ 2x² - 5x - 3 = 0 
⇒ 2x² - 6x + 1x - 3 = 0 
⇒ 2x(x - 3) + 1(x - 3) = 0 
⇒ (x - 3)(2x + 1) = 0 
⇒ x - 3 = 0
and, 
2x + 1 = 0 
⇒ x = 3 
or 2x = -1
So, the roots of the quadratic equation are 3 and -1/2. 

(iii) 

(iv) 3x² + 5√5x - 10 = 0 
⇒ 3x² + 5√5x - 10 = 0 
⇒ 3x² + 6√5x - √5 - 10 = 0 
⇒ 3x(x + 2√5) - √5(x + 2√5) = 0 
⇒ (x + 2√5)(3x - √5) = 0 
⇒ x = √5/3
or x = -2√5
So, these are the roots of the given quadratic equation. 

(v) 21x² - 2x + 1/21 = 0
⇒ 441x² - 42x + 1 = 0 
⇒ 441x² - 21x - 21x + 1 = 0 
⇒ 21x( 21x - 1) - 1(21x - 1) = 0 
⇒ (21x - 1)(21x - 1) = 0 
⇒ (21x - 1) = 0 or (21x - 1) = 0 
⇒ 21x = 1 or 21x = 1 
⇒ x = 1/21, 1/21 
So, the roots of the given equation are x = 1/21, 1/21