Exercise 4.1
Question 1: Check whether the following are quadratic equations :
(i) (x + 1)^2= 2(x – 3) (ii) x^2– 2x = (–2) (3 – x)
(iii) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x +1) = x(x + 5)
Solution:
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Question 1:
(v) (2x – 1)(x – 3) = (x + 5)(x – 1) (vi) x^2+ 3x + 1 = (x – 2)^2
(vii) (x + 2)^3= 2x (x^2– 1) (viii) x^3– 4x^2– x + 1 = (x – 2)^3
Solution:
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Question2: 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 plot.
Solution:
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Question2: (ii) The product of two consecutive positive integers is 306. We need to find the integers.
Solution:
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Question2: (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.
Solution:
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Question2: (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.
Solution: