#### Concept: Roots by Completing Squares

Find the roots of the following quadratic equations, if they exist, by the method of completing squares:

- 2x
^{2}- 7x + 3 = 0 - 2x
^{2}+ x – 4 = 0 - 4x
^{2}+ 4\\sqrt3)x + 3 = 0 - 2x
^{2}+ x + 4 = 0

- 2x
#### Concept: Roots by Quadratic Formula

Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula:

- 2x
^{2}- 7x + 3 = 0 - 2x
^{2}+ x – 4 = 0 - 4x
^{2}+ 4\\sqrt3)x + 3 = 0 - 2x
^{2}+ x + 4 = 0

- 2x
#### Concept: Find roots after framing quadratic equation

Find the roots of the following equations:

- x - \\frac{1}{x}) = 3, x ≠ 0
- \\frac{1}{x + 4}) - \\frac{1}{x - 7}) = \\frac{11}{30}), x ≠ -4, 7

#### Concept: Word Problem in Quadratic Equation

The sum of the reciprocals of Rehman’s ages ( in years) 3 years ago and 5 years from now is \\frac{1}{3}). Find his present age.

#### Concept: Word Problem in Quadratic Equation

In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of the marks would have been 210. Find her marks in the two subjects.

#### Concept: Frame Quadratic Equation & Find Roots

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

#### Concept: Frame Quadratic Equation & Find Roots

The difference between squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

#### Concept: Frame Quadratic Equation for Speed & Distance

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

#### Concept: Frame Quadratic Equation for Pipes & Tanks

Two water taps together can fill a tank in 9(\\frac{3}{8})) hours. The tap of larger dimensions 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.

#### Concept: Word Problem in Speed, Distance & Time

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.

#### Concept: Word Problem in Geometry - Sides of Squares

Sum of the areas of two squares is 468 m

^{2}. If the difference of their perimeter is 24 m, find the sides of the two squares.