Question 1 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2-6x+\frac{9}{2}=0$

Question 2 :
State True or False: Every quadratic equation has at most two roots.

Question 3 :
State True or False whether the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$

Question 4 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b60273b23058497998d.png' /> In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the length of the pond.

Question 5 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.

Question 6 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.

Question 7 :
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 8 :
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 10 :
Find the discriminant of the quadratic equation $2x^2 – 4x + 3 = 0$.