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.
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