Chapter 4 Quadratic Equations Ex 4.2

Chapter 4 Quadratic Equations Ex 4.2

Question 1.
Find the roots of the following quadratic equations by factorisation:
(i) x² -3x – 10 = 0
(ii) 2x² + x – 6 = 0
(iii) √2x² + 7x + 5√2 = 0
(iv) 2x² – x + 18 = 0 8
(v) 100 x² – 20 X + 1 = 0
Solution:

Question 2.
Solve the following situations mathematically:

(i) 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.
(ii) 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 ₹750. We would like to find out the number of toys produced on that day.
Solution:
(i) Let the number of marbles John had be x
Then, the number of marbles Jivanti had = 45 -x
The number of marbles left with John, when he lost 5 marbles = x – 5
The number of marbles left with Jivanti, when she lost 5 marbles = 45 -x – 5 = 40 -x

Question 3.
Find two numbers whose sum is 27 and product is 182.
Solution:
Let one number = x ,
∴ other number = 21 -x
According to question,

Question 4.
Find two consecutive positive integers, sum of whose squares is 365.
Solution:
Let the two consecutive integers be x and x + 1.
According to question,

Question 5.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solution:
Let base = x cm,
∴ height = (x – 7) cm
By Pythagoras Theorem,
(base)² + (height)² = (hypotenuse)²

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 ₹90, find the number of articles produced and the cost of each article.
Solution: