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Ex 4.1, 2 - Represent in form of quadratic equations - Making quadratic equation

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Ex 4.1 ,2 Represent the following situations in the form of quadratic equations : (i) The area of a rectangular plot is 528 m2. 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. Given that Area = 528 m2 and Length is one more that twice its breadth Let the breadth be x So, length = 2x + 1 We know that Area of rectangle = Length × breadth 528 = (2x + 1) x (2x + 1) x = 528 2x2 + x = 528 2x2 + x – 528 = 0 It is the form of ax2 + bx + c = 0 Where a = 2, b = 1 , c = –528 Hence, it is a quadratic equation . Ex 4.1 ,2 Represent the following situations in the form of quadratic equations : (ii) The product of two consecutive positive integers is 306. We need to find the integers. There is a difference of 1 in consecutive integers, Hence, Let the first integer = x Second integer = x + 1 Now , given that Product of integers = 306 First integer × Second integer = 306 x (x + 1) = 306 x2 + x = 306 x2 + x – 306 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = 1 , c = –306 Hence, it is a quadratic equation . Ex 4.1 ,2 Represent the following situations in the form of quadratic equations : (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 Rohan’s present age. Let Rohan's age = x Rohan’s mother age = x + 26 After 3 years Rohan’s age = x + 3 Rohan’s mother age = (x + 26) + 3 = x + 29 Now, Product of ages after 3 years = 360 (x + 3) (x + 29) = 360 x (x + 29) + 3 (x + 29) = 360 x2 + 29x + 3x + 87 = 360 x2 + 29x + 3x + 87 – 360 = 0 x2 + 32x – 273 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = 32 , c = –273 Hence, it is a quadratic equation . Ex 4.1 ,2 Represent the following situations in the form of quadratic equations : (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. Let the speed of train be x km/hr From (1) (x – 8) (480/𝑥 " + 3" ) = 480 (x – 8) ( (480 + 3𝑥)/𝑥) = 480 (x – 8) (480 + 3x) = 480 x x (480 + 3x) – 8 (480 + 3x) = 480 x 480x + 3x2 – 3840 – 24x = 480 x 480x + 3x2 – 384 – 24x – 480 x = 0 3x2 + 480x – 480x – 24x 3840 = 0 3x2 – 24x – 3840 = 0 3 (x2 – 8x – 1280) = 0 x2 – 8x – 1280 = 0/3 x2 – 8x – 1280 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = – 8 , c = –1280 Hence, it is a quadratic equation .

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