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.

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them :

2x² - 3x + 5 = 0

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them :

2x² - 6x + 3 = 0

Find the value of k for the following quadratic equation, so that it has two equal roots.

2x² + kx + 3 = 0