# Class 10 – Quadratic Equations – Important Questions

1. Find the roots of the equation 2x2– 5x + 3 = 0, by factorisation.
2. Write the discriminant of the quadratic equation (x + 5)2 = 2(5x – 3).
3. Using completing the square method, show that the equation x2 – 8x + 18 = 0 has no solution.
4. Find the roots of the quadratic equation 3x2 – 2√6x + 2 = 0.
5. Find the roots of the equation 5x2 – 6x – 2 = 0 by the method of completing the square.
6. A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m (see Fig. 4.3). Find its length and breadth.
7. Two water taps together can fill a tank in 9×3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
8. Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.