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) $2x^2 + 7x + 5 = 0$

(iv) $2x^2 - x + 8 = 0$

(v) $100x^2 - 20x + 1 = 0$

Solve the problems given in Example 1.

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 $\text{Rs. } 90$, find the number of articles produced and the cost of each article.