Formation of Quadratic Equation in One Variable

We will learn about the formation of quadratic equation in one variable from a mathematical problem.

Consider the following examples:

1. Length of a rectangular park is 40 metres more than its breadth. Area of the park is 2304 square metres.

Now we will learn how to express this statement in Mathematical language

Let the breadth of the rectangular park = x metres

Therefore, length of the rectangular park = (x+ 40) metres

So, area of the rectangular park = (x + 40) ∙ x square metres

According to the problem we get,

(x + 40) ∙ x = 2304

or, x^2 + 40x = 2304

or, x2  + 40x - 2304 = 0 .................... (i)

OR,

Let the length of the rectangular park = x metres

Therefore, the breadth of the rectangular park =(x - 40) metres

Area of the rectangular park = x(x - 40) square metres

According to the problem we get,

x(x - 40) = 2304

or,x2  - 40x - 2304 = 0 ....................  (ii)

Both of (i) and (ii) are quadratic equations.

2. Mike 3 hours more to do a piece of work than Davis. They together complete it in 2 hours.

Let Davis complete a piece of work in x hours

and Mike complete the same work in (x + 3) hours.

Therefore, in 1 hour Davis complete 1/x part of the work

and in 1 hour Make complete 1/(x + 3) part of the work.

Hence, in 1 hour they togetherly complete 1/x + 1/(x + 3) of the part.

According to the problem we get,

1/x + 1/(x + 3) = ½ ....................  (i)

Or,

Let Mike complete a piece of work in x hours

and Davis complete the same work in (x - 3) hours.

Therefore, in 1 hour Davis complete 1/(x - 3) part of the work.

and in 1 hour Mike complete 1/x part of the work

Hence, in 1 hour they togetherly complete 1/(x- 3) + 1/x of the part.

According to the problem we get,

1/(x - 3) + 1/x = ½ ....................  (ii)

Both of (i) and (ii) are quadratic equations.

Algebra/Linear Algebra

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Worksheet on Word Problems on Quadratic Equations by Factoring