Answer :

**(i)The area of a rectangular plot is 528 m ^{2}. **Let the breadth of the plot be

*x*m.

The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Thus, the length of the plot is (2

*x*+ 1) m.

Area of a rectangle = Length × Breadth

∴ 528 = *x* (2*x* + 1)

⇒ 2x^{2} + x – 528 = 0 (required quadratic form)

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

Let the consecutive integers be *x* and *x* + 1.

It is given that their product is 306.

∴ x (x+1) = 306

⇒ x^{2} + x – 306 = 0 (required quadratic form)

**(iii)** Let Rohan’s present age be

*x*.

Given, Rohan's Mother is 26 years older than him

Hence, his mother’s age = *x*+26

3 years hence,

Rohan’s age = *x* + 3

Mother’s age = *x* + 26 + 3

= *x* + 29

It is given that the product of their ages after 3 years is 360.

∴ (x+3) (x+29) = 360

x^{2}+ 3x + 29x + 87 = 360

⇒ x^{2} +32x – 273 = 0 (required quadratic form)

**(iv)** Let the speed of train be

*x*km/h.

As speed = distance / time

⇒ Time taken for travel 480 km =

In the second condition,

speed of train = (x – 8) km/h

Given that the train will take 3 hours more to cover the same distance.

Therefore, Time taken for traveling 480 km =

Speed × Time = Distance

= 480

⇒ 480 + 3x - - 24 = 480

⇒ 3x - = 24

⇒ 3x^{2}- 3840 = 24x

⇒ 3x^{2} – 24x - 3840 = 0

⇒ x^{2} – 8x - 1280 = 0 (required quadratic form)

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