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
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit the following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Analytical geometry calculators
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Ratio and proportion shortcuts
Converting repeating decimals in to fractions