Exercise 4.2

❓ Find the roots of the following quadratic equations by factorisation:
(i)$ x^2 – 3x – 10 = 0$
(ii) $2x^2 + x – 6 = 0$
(iii) $\sqrt{2} x^2 + 7 x+5\sqrt{ 2}= 0$
(iv) $2x^2 – x + \frac{1}{8} = 0$
(v) $100 x^2 – 20x + 1 = 0$

❓ (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.
(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 ₹ 750. We would like to find out the number of toys produced on that day.

❓ Find two numbers whose sum is 27 and product is 182.

❓ Find two consecutive positive integers, sum of whose squares is 365.

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

❓ 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.

Ch 4: Quadratic Equations

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