Question 1 :
Find the nature of the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$

Question 2 :
Find the roots of the equation $2x^2 – 5x + 3 = 0$, by factorisation.

Question 3 :
Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$

Question 4 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.

Question 6 :
Justify why the following quadratic equation has two distinct real roots: $\left(x+1\right)\left(x-2\right)+x=0$

Question 7 :
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.

Question 8 :
Find the roots of the following quadratic equation (by the factorisation method): $3\sqrt{2}x^2-5x-\sqrt{2}=0$

Question 9 :
Represent the following situation in the form of quadratic equations: A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Question 11 :
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the express train.

Question 12 :
Find the roots of the quadratic equation (by using the quadratic formula): $2x^2-3x-5=0$

Question 13 :
Is it possible to design a rectangular park of perimeter 80 m and area $400 m^2$ ? If so, find its length and breadth.

Question 14 :
Find two consecutive positive integers, sum of whose squares is 365.

Question 15 :
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 number of articles produced.

Question 18 :
Find the positive root of the equation $2x^2 + x - 300 = 0$, by factorisation.

Question 20 :
Represent the following situation in the form of a quadratic equation : The area of a rectangular plof is 528 $m^2$. The length of the plof (in metres) is one more than twice its breadth. We need to find the length and breadth of the plof.