Question 1 :
Justify why the following quadratic equation has no two distinct real roots: $x^2-3x+4=0$

Question 2 :
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, original average speed of the train is?

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

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

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

Question 7 :
Check whether the following is quadratic equation : $(x+2)^3 = 2x (x^2 - 1)$

Question 8 :
Is it possible to design a rectangular mango grove whose length is twice its breadth,and the area is $800 m^2$ ? If so, find its length and breadth.

Question 9 :
Check whether the following is quadratic equation : $x^2 + 3x + 1 = (x-2)^2$

Question 10 :
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 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 passenger train.

Question 12 :
State True or False: Every quadratic equation has at least one real root.

Question 13 :
Is the following situation possible? If so, determine their present ages.The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Question 15 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.

Question 16 :
Find the positive root of the equation $2x^2 + x - 300 = 0$, by factorisation.

Question 17 :
Check whether the following is a quadratic equation: $x(x + 1) + 8 = (x + 2) (x – 2)$

Question 18 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.

Question 19 :
Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$