RD Sharma Solutions for Class 10 Chapter 8 Quadratic Equations Exercise 8.1

RD Sharma Solutions Chapter 8 Quadratic Equations Exercise 8.1 Class 10 Maths

Chapter Name	RD Sharma Chapter 8 Quadratic Equations
Book Name	RD Sharma Mathematics for Class 10
Other Exercises	Exercise 8.2 Exercise 8.3 Exercise 8.4 Exercise 8.5 Exercise 8.6
Related Study	NCERT Solutions for Class 10 Maths

Exercise 8.1 Solutions

1. Which of the following are quadratic equations?

(i) x² + 6x – 4 = 0
(ii) √(3x²) – 2x + ½ = 0
(iii) x² + 1/x² = 5
(iv) x – 3/x = x²
(v) 2x² - √3x + 9 = 0
(vi) x² – 2x - √x – 5 = 0
(vii) 3x² – 5x + 9 = x² – 7x + 3
(viii) x + 1/x = 1
(ix) x² – 3x = 0
(x) (x + 1/x)² = 3(1 + 1/x) + 4
(xi) (2x + 1)(3x+ 2) = 6(x – 1)(x – 2)
(xii) x + 1/x = x² , x ≠ 0
(xiii) 16x² – 3 = (2x + 5)(5x – 3)
(xiv) (x + 2)³ = x³ – 4
(xv) x(x + 1) + 8 = (x +2)(x – 2)

Solution 
(i) x² + 6x – 4 = 0
(ii) √(3x²) – 2x + ½ = 0
(iii) x² + 1/x² = 5
(iv) x – 3/x = x²
(v) 2x² - √3x + 9 = 0
(vi) x² – 2x - √x – 5 = 0
(vii) 3x² – 5x + 9 = x² – 7x + 3
(viii) x + 1/x = 1
These are all quadratic equations.

2. In each of the following, determine whether the given values are solutions of the given equation or not: 
(i) x² – 3x + 2 = 0, x = 2, x = - 1
(ii) ax² - 3abx + 2b² = 0, x = a/b and x = b/a
(iii) x² - √2x - 4 = 0, x = - √2 and x = -8√2
(iv) 2x² – x + 9 = x² + 4x + 3, x = 2 and x = 3
(v) x + 1/2 = 13/6 = x = 5/6, x = 4/3
(vi) x² – 3√3x + 6 = 0, x = √3, x = -8√3
(vii) x² + x + 1 = 0, x = 0, x = 1

Solution

(i) x² – 3x + 2 = 0, x = 2, x = - 1

3. In each of the following, find the value of k for which the given value is a solution of the given equation:
(i) 7x² + kx - 3 = 0, x = 2/3 
(ii) x² - x(a + b) + k = 0, x = a
(iii) kx² + √2x - 4 0, x = √2
(iv) x² + 3ax + k = 0, x = -a

Solution

4. If x = 2/3  and x = -3 are the roots of the equation ax² + 7x + b = 0, find the values of a and b. 

Solution

a = 3, b = -6

5. Determine if, 3 is a root of the equation given below:
√(x² - 4x + 3) + √(x² - 9) = ² (4x² - 14x + 16)

Solution

Given to check whether 3 is a root of the equation