Slide12.JPG

Slide13.JPG
Slide14.JPG Slide15.JPG

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

Transcript

Ex 2.4, 3 If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b. For a cubic Polynomial p(x) = ax3 + bx2 + cx + d With zeroes Ξ±, 𝛽 and Ξ³ We have 𝛂 + 𝛽 + 𝛄 = (βˆ’π’ƒ)/𝒂 𝛂"𝛽" + 𝛽𝛄 + 𝛄𝛂 = 𝒄/𝒂 𝛂"𝛽" 𝛄= (βˆ’π’…)/𝒂 Now, p(x) = x3 βˆ’ 3x2 + x + 1 Comparing with p(x) = Ax3 + Bx2 + Cx + D, A = 1, B = βˆ’3, C = 1 and D = 1 Zeroes are 𝜢 = a βˆ’ b, 𝜷 = a and 𝜸 = a + b Sum of zeroes Sum of zeroes = (βˆ’π΅)/𝐴 𝜢 + 𝜷 + 𝜸 = (βˆ’π‘©)/𝑨 a βˆ’ b + a + a + b = 3 3a = 3 a = 1 Sum of Product zeroes Sum of Product zeroes = 𝐢/𝐴 𝜢𝜷+ 𝜷 𝜸 + 𝜸 𝜢 = π‘ͺ/𝑨 (a – b)a + a(a + b) + (a + b) (a βˆ’ b) = 1 a2 – ba + a2 + ab + a2 – b2 = 1 a2 + a2 + a2 βˆ’b2 = 1 3a2 βˆ’ b2 = 1 Putting a = 1 3(1)2 βˆ’ b2 = 1 3 βˆ’ b2 = 1 3 – 1 = b2 b2 = 2 b = Β± √𝟐 Thus, a = 1 and b = Β± √𝟐

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.