Question 4 :
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 5 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$

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

Question 7 :
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 8 :
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 9 :
Find the roots of the following quadratic equation by factorisation: $x^2 – 3x – 10 = 0$

Question 10 :
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present age of Asha.

Question 11 :
<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 12 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x – 4 = 0$

Question 13 :
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Question 16 :
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 express train.

Question 17 :
<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 :
A quadratic equation $ax^2 + bx + c =0$ has two equal real roots when :

Question 19 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.

Question 20 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2+x-1=0$

Question 21 :
If $b=0$, $c<0$, is it true that the roots of $x^2+bx+c=0$ are numerically equal and opposite in sign?

Question 22 :
Check whether the following is a quadratic equation: $x(2x + 3) = x^2 + 1$

Question 23 :
Find two numbers whose sum is 27 and product is 182.

Question 24 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 – 7x + 3 = 0$

Question 26 :
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Write an equation to find out how many marbles they had to start with.

Question 28 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $4x^2+4\sqrt{3}x+3=0$

Question 29 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$