Question 1 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $4x^2+4\sqrt{3}x+3=0$

Question 4 :
A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is?

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

Question 6 :
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Find out at what distances from the two gates should the pole be erected?

Question 7 :
Find the roots of the quadratic equation (by using the quadratic formula): $5x^2+13x+8=0$

Question 8 :
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 passenger train.

Question 9 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$

Question 10 :
Justify why the following quadratic equation has no two distinct real roots: $x^2-3x+4=0$

Question 11 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.

Question 12 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$

Question 14 :
State True or False: Every quadratic equation has at least two roots.

Question 15 :
Check whether the following is a quadratic equation: $(x – 2)^2 + 1 = 2x – 3$

Question 16 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.

Question 17 :
A quadratic equation $ax^2 + bx + c =0$ has two equal real roots when :

Question 18 :
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 19 :
Find the roots of the following quadratic equation (by the factorisation method): $\frac{2}{5}x^2-x-\frac{3}{5}=0$

Question 20 :
Find the roots of the quadratic equation (by using the quadratic formula): $-3x^2+5x+12=0$