Exercise 4.2

Find the roots of the following quadratic equations by factorization.

Find the roots of the following quadratic equations by factorization.

Find the roots of the given quadratic equation by factorisation:

$2x^2-x+\frac{1}{8}=0$

Find the roots of the given quadratic equations by factorisation:

Represent the following situations mathematically.

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

The altitude of a right triangle is $7 \mathrm{c}\mathrm{m}$ less than its base. If the hypotenuse is $13 \mathrm{c}\mathrm{m}$, 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 $\mathrm{₹}90$, find the number of articles produced and the cost of each article.