Writing the Given Statement into a Quadratic Equation and Solve them :
In this section, we will see some example problems to show how to write the given statement into a quadratic equation.
Example 1 :
Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m². The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.
Area of rectangular plot = 528 m²
let "x" be the breadth of the plot
length of the plot = 2 x + 1
length ⋅ breadth = 528
(2 x + 1) x = 528
2 x² + x - 528 = 0
This the required quadratic equation.
Example 2 :
the product of two consecutive positive integers is 306. We need to find the integers.
Let x and x + 1 are the two consecutive positive integers
product of these integers = 306
x (x + 1) = 306
x² + x = 306
x² + x - 306 = 0
Example 3 :
Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.
Let "x" be Rohan's age
Let "x + 26" be Rohan's mother's age
Three years later Rohan and his mother ages will be x + 3 and x + 29 respectively
(x + 3) (x + 29) = 360
x² + 29 x + 3 x + 87 = 360
x² + 32 x + 87 - 360 = 0
x² + 32 x - 273 = 0
Example 4 :
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Distance to be covered = 480 km
Speed of the train = x km/hr
Time = Distance/speed
Time taken by the train to cover 480 km distance in x km/hr = 480/x
Time taken by the train to cover 480 km distance in 8 km/hr less speed = 480/(x - 8)
3 = [480/x] - [480/(x - 8)]
3 = 480 [ (1/x) - (1/(x-8))]
3/480 = [(x - 8 - x)/(x(x - 8))]
1/160 = -8/(x² - 8 x)
(x² - 8 x) = -8 (160)
x² - 8 x + 1280 = 0
After having gone through the stuff and examples, we hope that the students would have understood, writing the given statement into a quadratic equation
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