Mathematics is like music – Enjoy it!!!
Concept: In this tutorial, you will understand what is a Linear, Quadratic and Cubic polynomial and also what is a zero of a polynomial and its geometric meaning. Concepts are explained with examples and graphically. Concept: Relationship between zeroes and…
Read MoreQuestion 1: Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : (i) p(x) = x3 – 3×2 + 5x – 3, g(x) = x2 – 2 (ii) p(x) =…
Read MoreQuestion 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x2 –2x–8 (ii) 4s2 –4s+1 (iii) 6×2 –3–7x (iv) 4u2 +8u (v) t2 –15 (vi) 3×2 –x–4 Question 2:…
Read MoreExample 1: Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x). Example 2: Find the…
Read MoreQuestion 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: Question 2: Write down the decimal expansions of those rational numbers in Question 1…
Read MoreQuestion 1: Prove that √5 is irrational. Question 2: Prove that 3 + √5 is irrational. Question 3: Prove that the following are irrationals:(i) 1/√2 (ii) 7√5 (iii) 6 + √2 Class 10 | Exercise 1.2 Class 10 | Exercise…
Read MoreQuestion 1: Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Question 2: Find the LCM and HCF of the following pairs of integers and verify that LCM ×…
Read MoreQuestion 1: Use Euclid’s division algorithm to find the HCF of :(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Question 2: Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5,…
Read MoreExample 1 : Use Euclid’s algorithm to find the HCF of 4052 and 12576. Example 2: Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1,…
Read MoreTheorem 1.1 (Euclid’s Division Lemma) : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b. Euclid’s Division Algorithm : This algorithm is used to find…
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