Question 1 :
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 2 :
Using method of completing the square , $3x^2-5x+2=0$ can be written as ?

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

Question 8 :
A quadratic equation $ax^2 + bx + c =0$ has two equal real roots when :

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

Question 10 :
State true or false: $b^2 – 4ac$ is called the discriminant of the quadratic equation $ax^2 + bx + c = 0$.

Question 11 :
Using method of completing the square , solve for x: $5x^2-6x-2=0$

Question 12 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is

Question 13 :
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 14 :
Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by the method of completing the square?

Question 15 :
State True or False whether the following quadratic equation has two distinct real roots: $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$

Question 16 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998e.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 breadth of the pond.

Question 18 :
Using method of completing the square , solve for x: $2x^2-5x+3=0$

Question 19 :
Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$

Question 20 :
Represent the following situation in the form of a quadratic equation : The area of a rectangular plof is 528 $m^2$. The length of the plof (in metres) is one more than twice its breadth. We need to find the length and breadth of the plof.