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

Find area of the triangle with vertices at the point given in each of the following : (i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8) (iii) (-2, -3), (3, 2), (-1, -8)

Show that points A (a, b + c ), B (b, c + a ), C (c, a + b ) are collinear.

Solve the problems given in Example 1.

Find values of k if area of triangle is 4 sq. units and vertices are (i) (k, 0), (4, 0), (0, 2) (ii) (-2, 0), (0, 4), (0, k)

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

(i) Find equation of line joining (1, 2) and (3, 6) using determinants. (ii) Find equation of line joining (3, 1) and (9, 3) using determinants.

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

If area of triangle is 35 sq units with vertices (2, - 6), (5, 4) and (k, 4). Then k is (A) 12 (B) -2 (C) -12, -2 (D) 12, -2

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.