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 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 8.1 Solutions
1. Which of the following are quadratic equations?
(i) x^{2} + 6x – 4 = 0
(ii) √(3x^{2}) – 2x + ½ = 0
(iii) x^{2} + 1/x^{2} = 5
(iv) x – 3/x = x^{2}
(v) 2x^{2}  √3x + 9 = 0
(vi) x^{2} – 2x  √x – 5 = 0
(vii) 3x^{2} – 5x + 9 = x^{2} – 7x + 3
(viii) x + 1/x = 1
(ix) x^{2} – 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 = x^{2} , x ≠ 0
(xiii) 16x^{2} – 3 = (2x + 5)(5x – 3)
(xiv) (x + 2)^{3} = x^{3} – 4
(xv) x(x + 1) + 8 = (x +2)(x – 2)
Solution
(i) x^{2} + 6x – 4 = 0
(ii) √(3x^{2}) – 2x + ½ = 0
(iii) x^{2} + 1/x^{2} = 5
(iv) x – 3/x = x^{2}
(v) 2x^{2}  √3x + 9 = 0
(vi) x^{2} – 2x  √x – 5 = 0
(vii) 3x^{2} – 5x + 9 = x^{2} – 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) x^{2} – 3x + 2 = 0, x = 2, x =  1
(ii) ax^{2}  3abx + 2b^{2} = 0, x = a/b and x = b/a
(iii) x^{2}  √2x  4 = 0, x =  √2 and x = 8√2
(iv) 2x^{2} – x + 9 = x^{2} + 4x + 3, x = 2 and x = 3
(v) x + 1/2 = 13/6 = x = 5/6, x = 4/3
(vi) x^{2} – 3√3x + 6 = 0, x = √3, x = 8√3
(vii) x^{2} + x + 1 = 0, x = 0, x = 1
Solution
(i) x^{2} – 3x + 2 = 0, x = 2, x =  1
(i) 7x^{2} + kx  3 = 0, x = 2/3
(ii) x^{2}  x(a + b) + k = 0, x = a
(iii) kx^{2} + √2x  4 0, x = √2
(iv) x^{2} + 3ax + k = 0, x = a
√(x^{2}  4x + 3) + √(x^{2}  9) = ^{2} (4x^{2}  14x + 16)