Chapter 2 Polynomials Exercise 2.1
Chapter 2 Polynomials Exercise 2.1 Question 1. The graphs of y = p(x) are given in figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. Solution: The number of zeroes of p(x) in each graph given; are
Chapter 1 Real Numbers Ex 1.4
Chapter 1 Real Numbers Ex 1.4 Question 1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: Solutions: Question 2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. Solutions: In […]
Chapter 1 Real Numbers Ex 1.3
Chapter 1 Real Numbers Ex 1.3 Question 1. Prove that √5 is irrational. Solutions: Question 2. Prove that 3 + 2√5 is irrational. Solutions: Let us assume that 3 + 2√5 is rational. ∴ There exists co-prime integers a and b(b ≠ 0) such that But this contradicts the fact that √5 is irrational. This […]
Chapter 1 Real Numbers Ex 1.2
Chapter 1 Real Numbers Ex 1.2 Question 1. Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429. Solutions: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429.So, 7429 = 17 x 19 x 23 Question 2. Find the LCM and HCF of the […]
Chapter 1 Real Numbers Ex 1.1
Chapter 1 Real Numbers Ex 1.1 Question 1. Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255. Solutions: (i) Given numbers are 135 and 225. On applying Euclid’s division algorithm, we have 225 = 135 x 1 + 90 Since the remainder 90 ≠ […]