(i) The area of 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 .

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

(iii) Rohan’s mother is 26 years older than him. The products of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(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.

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(i)Let the breadth of the plot is x meters
Then, the length is (2x + 1) meters.
Area = length × breadth
528 = x × (2x + 1)
528 = 2x2 + x
2x2 + x – 528 = 0

(ii)Let x and x+1 be two consecutive integers.
Then, x(x + 1) = 306
x2 + x – 306 = 0

(iii)Let x be the Rohan’s present age. Then, his mother’s present age is x+26
After 3 years theirs ages will be x+3 and x+26+3 = x+29 respectively.
Hence,
(x+3)(x+29) = 360
x2+3x+29x+87 = 360
x2+32x- 273 = 0

(iv)

Let speed of train be x km/h

Time taken by train to cover 480 km = 480xhours

If, speed had been 8km/h less then time taken would be (480x−8) hours

According to given condition, if speed had been 8km/h less then time taken is 3 hours less.

Therefore, 480x – 8 = 480x + 3

⇒480 (1x – 8 − 1x) = 3

⇒480 (x – x + 8) (x) (x − 8) = 3

⇒480 × 8 = 3 (x) (x − 8)

⇒x2 - 8x = 1280

⇒x2 - 8x - 1280 = 0

⇒x(x - 40) + 32(x - 40) = 0

⇒(x + 32)(x - 40 ) = 0

⇒ x = 40 or, x = -32

so,x = 40

This is a Quadratic Equation.

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