CBSE Class 10 Mathematics Quadratic Equations Worksheet Set A

Very Short Answer type Questions

Question. Check whether the following are quadratic equations :
(i) (2x – 1)(x – 3) = (x + 5)(x – 1), (ii) (x + 2)3 = 2x (x² – 1)
Answer : (i) YES (ii) NO

Question. Two water taps together can fill a tank in 9(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.
Answer : 15 hours, 25 hours

Question. Represent the following situation in the form of quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.
Answer : x² + 32x – 273 = 0, where x (in years) is the present age of Rohan.

Question. Represent the following situation in the form of quadratic equation : 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. We would like to find out how many marbles they had to start with.
Answer : x² – 45x + 324 = 0, where x is the number of marbles John had.

Question. 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 number of articles produced and the cost of each article.
Answer : Number of articles = 6, Cost of each article = Rs 15

Question. Represent the following situation in the form of quadratic equation : A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Answer : x² – 55x + 750 = 0, where x is the number of toys produced.

Question. Find the roots of the quadratic equation : 6x² – x – 2 = 0.
Answer : 2/3, 1/2

Question. Find the nature of the roots of the quadratic equation 2x² – 6x + 3 = 0. If the real roots exist, find the
Answer : Distinct roots; 3±√3/2

Question. Find the roots of the quadratic equation : 2x² – x + 1/8 = 0
Answer : 1/4, 1/4

Question. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Answer : 120 m, 90 m

Question. Represent the following situation in the form of quadratic equation : Rohan’s mother 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.
Answer : x² + x – 306 = 0, where x is the smaller integer

Question. Find the roots of the quadratic equation : √3x² − 2 √6 x + 2 = 0 .
Answer : √2/3,√2/3

Please click on below link to download CBSE Class 10 Mathematics Quadratic Equations Worksheet Set A