(1) Find the roots of the following quadratic equations by factorization:

(i) x^{2} - 3 x - 10 = 0 Solution

(ii) 2x^{2} + x - 6 = 0 Solution

(iii) √2x^{2} + 7 x + 5 √2 = 0 Solution

(iv) 2x^{2} - x + (1/8) = 0 Solution

(v) 100x^{2} - 20 x + 1 = 0 Solution

(2) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they have now is 124. We would like to find out how many marbles they had to start with. Solution

(3) 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, the total cost of production was $750. We would like to find the number of toys produced on that day.

(3) Find two numbers whose sum is 27 and product is 182.

(4) Find two consecutive positive integers,sum of whose squares is 365. Solution

(5) The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13 cm, find the other two sides. Solution

(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

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