Class 10 Mathematics

Quadratic Equation

Exercise 4.1 (NCERT) Part 2

Represent the following situation in the form of quadratic equation:

(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.

Solution: Let us assume breadth `= x`

Therefore; length `= 2x + 1`

Since area `= text(length) xx text(breadth)`

Hence; `x(2x + 1) = 528`

Or, `2x^2 + x = 528`

Or, `2x^2 + x – 528 = 0`


(ii) The product of two consecutive positive integers is 306. We need to find the integers.

Solution: Let us assume the first integer `= x`

Hence; second integer `= x + 1`

As per question; `x(x + 1) = 306`

Or, `x^2 + x = 306`

Or, `x^2 + 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 the Rohan’s age.

Solution: Let us assume, Rohan’s present age `= x`

So, his mother’s present age `= x + 26`

Three years from now, Rohan’s age `= x + 3`

Three years from now, mother’s age `= x + 29`

As per question; `(x + 3)(x + 29) = 360`

Or, `x^2 + 29x + 3x + 87 = 360`

Or, `x^2 + 32x + 87 = 360`

Or, `x^2 + 32x + 87 – 360 = 0`

Or, `x^2 + 32x – 273 = 0`


(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Solution: Let us assume, speed of train `= x` km/h

Therefore; reduced speed `= x – 8` km/h

We know, `text(time) = text(distance)/(speed)`

Hence;

`t=(480)/(x)`-------(1)

In case of reduced speed;

`t+3=(480)/(x-8)`

Or, `t=(480)/(x-8)-3` -----------(2)

From equations (1) and (2);

`(480)/(x)=(480)/(x-8)-3`

Or, `(480)/(x)=(480-3(x-8))/(x-8)`

Or, `(480)/(x)=(480-3x+24)/(x-8)`

Or, `480(x-8)=x(504-3x)`

Or, `480x-3840=504x-3x^2`

Or, `480x-3840-504x+3x^2=0`

Or, `3x^2-24x-3840=0`

Or, `x^2-8x-1280=0`


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Exercise 4.1(1)

Exercise 4.2(1)

Exercise 4.2(2)

Exercise 4.2(3)

Exercise 4.3(part1)

Exercise 4.3(part2)

Exercise 4.3(part3)

Exercise 4.3(part4)

Exercise 4.3(part5)

Exercise 4.4(part1)

Exercise 4.4(part2)