Exercise 4.2
1. Find the roots of the following quadratic equations by factorisation:
(i) x^2– 3x – 10 = 0 (ii) 2x^2+ x – 6 = 0
(iii) √ 2x^2 + 7x = 5√ 2 = 0 (iv) 2x^2– x +1/8 = 0
(v) 100x^2– 20x + 1 = 0
Solution:
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Question 2. Solve the problems given in Example 1.
(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
Solution:
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Question 2. Solve the problems given in Example 1.
(ii) A cottage industry produces a certain number of toys in a day. The cost of
production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was
Rs 750. We would like to find out the number of toys produced on that day
Solution:
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Question3. Find two numbers whose sum is 27 and product is 182.
Solution:
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Question 4. Find two consecutive positive integers, sum of whose squares is 365.
Solution:
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Question 5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solution:
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Question 6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹90, find the number of articles produced and the cost of each article.
Solution: