In this post, we represent a given situation in the form of a quadratic equation.
The post has answers for 2nd problem in Exercise 4.1, given in X grade, NCERT book.
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.
Substituting l by (2b + 1) in the formula
Convert equation to the quadratic equation form ax2 + bx + c = 0.
So the given situation can be expressed in the form of a quadratic expression as 2b2 + b – 528 = 0
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
Let the first integer be “x”
So the next consecutive integer will be “x+1”
It is given that the product of the two integers are 306
Convert equation to the quadratic equation form ax2 + bx + c = 0.
So the given problem can be expressed in the form of a quadratic expression as x2 + x – 306 = 0
(iii) 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 the present age of Rohan age be x years
Then Rohan’s Mother age will be x+26 years
After 3 years ,
Rohan’s age will be x+3 years
Rohan’s Mother age will be = x+26+3 = x+29
Let us put all the info in a tabular form for easy understanding
Convert equation to the quadratic equation form
ax2 + bx + c = 0.
So the given problem can be expressed in the form of a quadratic expression as x2 + 32x – 273 = 0
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Given :
The distance travelled by the train : 480km
Let the speed of the train be x km per hour.
Reduced speed = x-8
Distance formula :
Distance = Speed * Time
Or
Time = Distance /Speed
Time taken by train to cover 480 km at a speed of x km/hour = 480/x.
Time taken by train to cover the same distance at reduced speed = 480/(x-8).
It is given that it takes 3 more hours than the usual time when the speed is reduced
So the given problem can be expressed in the form of a quadratic expression as x2 – 8x – 1280 = 0