## Chapter 8 Quadratic Equations R.D. Sharma Solutions for Class 10th Math Exercise 8.5

1. Write the discriminant of the following quadratic equation:

(i) 2x2 - 5x + 3 = 0

Solution

(ii) x2 + 2x + 4 = 0

Solution

(iii) (x-2) (2x-1) = 0

Solution

(iv)  x2 - 2x + k = 0, k∈R

Solution

(v) √3 x2 + 2√2 x + 2√3 = 0

Solution

(vi) x2 - x + 1 = 0

Solution

(vii) 3x2 + 2x + k = 0

Solution

(viii) 4x2 - 3kx + 1 = 0

Solution

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

(i) 16x2 = 24x + 1

Solution

(ii) x2 + x + 2 = 0

Solution

(iii) √3 x2 + 10x - 8√3 = 0

Solution

(iv)  3x2 - 2x + 2 = 0

Solution

(v) 2 x2 - 2√6 x + 3 = 0

Solution

(vi) 3a2x2 + 8abx + 4b2 = 0, a≠0

Solution

(vii) 3x2 + 2√b x - b = 0

Solution

(viii) x2 - 2x + 1 = 0

Solution

(vii) 2x2 + 5√3 - 6 = 0

Solution

(x) √2 x2 + 7x + 5√2 = 0

Solution

(xi) 2x2 + 2√x + 1 = 0

Solution

(xii) 3x2 + bx + 2 = 0

Solution

3. Solve for x :

(i) (x-1)/(x-2) + (x-3)/(x-4) = 3⅓; x ≠ 2, 4

Solution

(ii) 1/x + 2/(2x-3) = 1/(x-2); x ≠ 0, 3/2, 2

Solution

(iii) x + 1/x = 3; x ≠ 0

Solution

(iv) 16/x -1 = 15/(x+1), x ≠ 0, -1

Solution

(v) 1/(x-3) - 1/(x+5) = 1/6, x ≠ 3, -5

Solution