Find the roots of the following quadratic equations by factorisation:
(i) \(x^2 - 3x - 10 = 0\)
(ii) \(2x^2 + x - 6 = 0\)
(iii) \(\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0\)
(iv) \(2x^2 - x + \frac{1}{8} = 0\)
(v) \(100x^2 - 20x + 1 = 0\)
(i) \(-2, 5\)
(ii) \(-2, \frac{3}{2}\)
(iii) \(-\frac{5}{\sqrt{2}}, -\sqrt{2}\)
(iv) \(\frac{1}{4}, \frac{1}{4}\)
(v) \(\frac{1}{10}, \frac{1}{10}\)
Solve the problems given in Example 1.
(i) \(9, 36\)
(ii) \(25, 30\)
Find two numbers whose sum is 27 and product is 182.
Numbers are 13 and 14.
Find two consecutive positive integers, the sum of whose squares is 365.
Positive integers are 13 and 14.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
5 cm and 12 cm
A cottage industry produces a certain number of pottery articles in a day. The cost of production of each article is 3 rupees more than twice the number of articles produced that day. If the total cost of production is ₹90, find the number of articles produced and the cost of each article.
Number of articles = 6, Cost of each article = ₹15