Question 1 :
Find the roots of the following quadratic equation (by the factorisation method): $21x^2-2x+\frac{1}{21}=0$

Question 2 :
Using method of completing the square , solve for x: $2x^2-5x+3=0$

Question 3 :
Represent the following situation in the form of a quadratic equation : A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h lesss, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Question 4 :
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 Rs. 90, find the cost of each article?

Question 5 :
Check whether the following is quadratic equation : (x - 2)(x +1)=(x - 1)(x + 3)

Question 6 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$

Question 7 :
What are the roots of $6x^2-\sqrt{2}x-2=0$ (by the factorisation of the corresponding quadratic polynomial)?

Question 8 :
Does the following equation has the sum of its roots as 3? $3x^2-3x+3=0$

Question 9 :
Find two numbers whose sum is 27 and product is 182.

Question 10 :
Check whether the following is a quadratic equation: $x(x + 1) + 8 = (x + 2) (x – 2)$