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Answer :
(i) A rectangular plot with area 528 \(m^2\) is given.
Let breadth of rectangular plot be x metres
Length is one more than twice its breadth.
Therefore, length of rectangular plot is \(2x + 1\) metres
Area of rectangle = length × breadth
=> \(528 = x (2x + 1)\)
=> \(528 = 2x^2 + x\)
=>\( 2x^2 + x – 528 = 0\)
This is the Quadratic Equation.
(ii) Let two consecutive numbers be x and (x + 1).
It is given that \(x (x + 1) = 306\)
=>\(x^2 + x = 306\)
=>\( x^2 + x – 306 = 0\)
This is the Quadratic Equation.
(iii) Let present age of Rohan = x years
Let present age of Rohan’s mother = \(x + 26\) years
Age of Rohan after 3 years = \(x + 3\) years
Age of Rohan’s mother after 3 years = \(x + 26 + 3 = (x + 29)\) years
According to given condition:
\((x + 3) (x + 29) = 360\)
=>\(x^2 + 29x + 3x + 87 = 360\)
=>\(x^2 + 32x - 273 = 0\)
This is the Quadratic Equation.
(iv) Let speed of train be x km/h
Time taken by train to cover 480 km = \(\frac{480}{x}\) hours
If, speed had been 8km/h less then time taken would be \(\frac{480}{x - 8}\) hours.
According to given condition, if speed had been 8km/h less then time taken is 3 hours less.
Therefore, \(\frac{480}{x – 8} = \frac{480}{x} + 3\)
=>\( 480 (\frac{1}{x – 8} - \frac{1}{x}) = 3\)
=>\( 480 (x – x + 8) = 3 (x) (x - 8) \)
=>\( 480 × 8 = 3 (x) (x - 8)\)
=>\( 3840 = 3x^2 - 24x\)
=>\(3x^2 - 24x - 3840 = 0\)
Dividing equation by 3, we get
=>\(x^2 - 8x - 1280 = 0\)
This is the Quadratic Equation.