Represent the following situations in the form of quadratic equations :(i) The area of a rectangular plot is 528 `m^2`. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plo

Explanation

(i) Let the breadth of the plot = x m
Then, the length of the plot = (2x+1)m
Now, area of rectangle = length`xx`breadth
`:.(2x+1)x=528`
`implies2x^(2)+x-528=0`
which is the required quadratic equation.
(ii) Let the two consecutive positive integers be x and x+1
`:.x((x+1)=306`
`impliesx^(2)+x=306`
`implies2x^(2)+x-528=0`
which is the required quadratic equation.
(iii) Let the age of Rohan be x years
Then, his mother's age =(x + 26) years
After 3 years,
Rohan's age = (x + 3) years
Rohan's mother age = `[(x+26)+3)]=(x+29)` years
`:.(x+3)(x+29)=360`
`impliesx^(2)+29x+3x+87=360`
`impliesx^(2)+32x-273=0`
which is the required quadratic equation.
(iv) Let the speed of the train be x km/hr.
Distance travelled by the train =480 km
:. Time taken to travel 480 km `=(480)/(x)hr" "[:'"Speed"=("Distance")/("Time")]`
If the speed had beed 8 km/hr less i.e.,(x-8)km/hr
:. Time taken to travel 480 km `(480)/(x-8)hr` Now, according to given condition
`(480)/(x-8)-(480)/(x)=3`
`implies(480x-480x+3840)/(x(x-8))=3implies3840=3x(x-8)`
`implies3840=3x^(3)-24x`
`implies3x^(2)-24x-3840=0`
`impliesx^(2)-8x-1280=0`
which is the required quadratic equation.