Slide1.JPG

Advertisement

Slide2.JPG

Advertisement

Slide3.JPG Slide4.JPG

 

 

  1. Chapter 2 Class 10 Polynomials (Term 1)
  2. Serial order wise

Transcript

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Ÿ/๐Ÿ p(๐Ÿ/๐Ÿ) = 2 (1/2)^3 + (1/2)^2 โˆ’ 5 (1/2) + 2 = 1/4 + 1/4 โˆ’ 5/2 + 2 = (1 + 1 โˆ’ 10 + 8)/4 = 0/4 = 0 Since p(1/2) = 0 โˆด ๐Ÿ/๐Ÿ is a zero of p(x) At x = ๐Ÿ p(1) = 2(1)3 + (1)2 โ€“ 5(1) + 2 = 2 + 1 โˆ’ 5 + 2 = 5 โˆ’ 5 = 0 Since p(1) = 0 โˆด 1 is a zero of p(x) At x = โ€“2 p(-2) = 2(-2)3 + (-2)2 โ€“ 5(-2) + 2 = 16 + 4 + 10 + 2 = โˆ’16 + 16 = 0 Since p(-2) = 0 โˆด โ€“2 is a zero of p(x). At x = ๐Ÿ/๐Ÿ p(๐Ÿ/๐Ÿ) = 2 (1/2)^3 + (1/2)^2 โˆ’ 5 (1/2) + 2 = 1/4 + 1/4 โˆ’ 5/2 + 2 = (1 + 1 โˆ’ 10 + 8)/4 = 0/4 = 0 Since p(1/2) = 0 โˆด ๐Ÿ/๐Ÿ is a zero of p(x) Verifying relationship between zeroes and coefficients For p(x) = 2x3 + x2 โˆ’ 5x + 2 a = 2, b = 1, c = โˆ’5 and d = 2 And zeroes are ๐œถ = 1/2, ๐œท = 1 and ๐œธ = โˆ’2 For a cubic Polynomial p(x) = ax3 + bx2 + cx + d With zeroes ฮฑ, ๐›ฝ and ฮณ We have ๐›‚ + ๐›ฝ + ๐›„ = (โˆ’๐’ƒ)/๐’‚ ๐›‚"๐›ฝ" + ๐›ฝ๐›„ + ๐›„๐›‚ = ๐’„/๐’‚ ๐›‚"๐›ฝ" ๐›„= (โˆ’๐’…)/๐’‚ Now ๐œถ+ ๐œท + ๐œธ = 1/2 + 1 โˆ’ 2 = (1 + 2 โˆ’ 4)/2 = (โˆ’1)/2 = (โˆ’๐’ƒ)/๐’‚

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.