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Last updated at Aug. 2, 2021 by

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Ex 2.4, 1 (Optional) - Polynomials Class 10 Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeros and the coefficients in each case: (i) 2x^3 + x^2 - 5x + 2; 1/2, 1, -2 At x = ๐/๐ p(๐/๐) = 2 (1/2)^3 + (1/2)^2 โ 5 (1/2) + 2 = 1/4 + 1/4 โ 5/2 + 2 = (1 + 1 โ 10 + 8)/4 = 0/4 = 0 Since p(1/2) = 0 โด ๐/๐ is a zero of p(x) At x = ๐ p(1) = 2(1)3 + (1)2 โ 5(1) + 2 = 2 + 1 โ 5 + 2 = 5 โ 5 = 0 Since p(1) = 0 โด 1 is a zero of p(x) At x = โ2 p(-2) = 2(-2)3 + (-2)2 โ 5(-2) + 2 = 16 + 4 + 10 + 2 = โ16 + 16 = 0 Since p(-2) = 0 โด โ2 is a zero of p(x). At x = ๐/๐ p(๐/๐) = 2 (1/2)^3 + (1/2)^2 โ 5 (1/2) + 2 = 1/4 + 1/4 โ 5/2 + 2 = (1 + 1 โ 10 + 8)/4 = 0/4 = 0 Since p(1/2) = 0 โด ๐/๐ is a zero of p(x) Verifying relationship between zeroes and coefficients For p(x) = 2x3 + x2 โ 5x + 2 a = 2, b = 1, c = โ5 and d = 2 And zeroes are ๐ถ = 1/2, ๐ท = 1 and ๐ธ = โ2 For a cubic Polynomial p(x) = ax3 + bx2 + cx + d With zeroes ฮฑ, ๐ฝ and ฮณ We have ๐ + ๐ฝ + ๐ = (โ๐)/๐ ๐"๐ฝ" + ๐ฝ๐ + ๐๐ = ๐/๐ ๐"๐ฝ" ๐= (โ๐ )/๐ Now ๐ถ+ ๐ท + ๐ธ = 1/2 + 1 โ 2 = (1 + 2 โ 4)/2 = (โ1)/2 = (โ๐)/๐

Chapter 2 Class 10 Polynomials (Term 1)

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.