Question 1 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$

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

Question 4 :
Find the roots of the quadratic equation (by using the quadratic formula): $2x^2-3x-5=0$

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

Question 6 :
Represent the following situation in the form of quadratic equations : The area of a rectangular plot is $528 m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Question 7 :
Check whether the following is a quadratic equation: $x^2 – 2x = (–2) (3 – x)$

Question 8 :
Check whether the following is quadratic equation : $x^3 - 4x^2 - x + 1 = (x-2)^3$

Question 9 :
Represent the following situation in the form of a quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.

Question 10 :
Check whether the following is quadratic equation : (x-3)(2x + 1)= x(x+5)