# 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 8.2Exercise 8.3Exercise 8.4Exercise 8.5Exercise 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

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