Question 1 :
Find the roots of the quadratic equation (by using the quadratic formula): $2x^2-3x-5=0$

Question 2 :
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Question 3 :
Find the roots of the quadratic equation $3x^2 - 2\sqrt{6}x+2=0$, by factorisation.

Question 4 :
Represent the following situation in the form of a quadratic equation : Rohan’s mofher is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Question 5 :
Two water taps together can fill a tank in $9{\frac{3}{8}}$ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Question 6 :
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 7 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x – 4 = 0$

Question 8 :
State true or false: A quadratic equation in the variable x is an equation of the form $ax^2 + bx + c = 0$, where a, b and c are real numbers and a≠ 0.

Question 10 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$