RD Sharma Chapter 4 : Quadratic Equation – Exercise 4.5 Solutions (Step-by-Step Guide)

1. Write the discriminant of the following quadratic equations:

   (i) 2x² − 5x + 3 = 0 Watch Solution

   (ii) x² + 2x + 4 = 0 Watch Solution

   (iii) (x − 1)(2x − 1) = 0 Watch Solution

  (iv) x² − 2x + k = 0, k ∈ R Watch Solution

  (v) √3x² + 2√2x − 2√3 = 0 Watch Solution

  (vi) x² − x + 1 = 0 Watch Solution

   (vii) (x + 5)² = 2(5x − 3)  Watch Solution

2. In the following, determine whether the given quadratic equations have real roots and if so, find the roots:

  (i) 16x² = 24x + 1 Watch Solution

  (ii) x² + x + 2 = 0 Watch Solution

  (iii) √3x² + 10x − 8√3 = 0 Watch Solution

  (iv) 3x² − 2x + 2 = 0 Watch Solution

  (v) 2x² − 2√6x + 3 = 0 Watch Solution

  (vi) 3a²x² + 8abx + 4b² = 0, a ≠ 0 Watch Solution

  (vii) 3x² + 2√5x − 5 = 0 Watch Solution

  (viii) x² − 2x + 1 = 0 Watch Solution

  (ix) 2x² + 5√3x + 6 = 0 Watch Solution

  (x) √2x² + 7x + 5√2 = 0 Watch Solution

  (xi) 2x² − 2√2x + 1 = 0  Watch Solution

  (xii) 3x² − 5x + 2 = 0 Watch Solution

3. Solve for x:

  (i) (x − 1)/(x − 2) + (x − 3)/(x − 4) = 3 1/3 , x ≠ 2, 4  Watch Solution

  (ii) 1/x + 2/(2x − 3) = 1/(x − 2) , x ≠ 0, 3/2, 2 Watch Solution

  (iii) x + 1/x = 3 , x ≠ 0 Watch Solution

  (iv) 16/x − 1 = 15/(x + 1) , x ≠ 0, −1  Watch Solution

  (v) 1/(x − 3) − 1/(x + 5) = 1/6 , x ≠ 3, −5 Watch Solution