Question 28 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 20, 2024 by Teachoo

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Question 28 If 𝛼 and 𝛽 are zeroes of a polynomial 6𝑥2 − 5x + 1 then form a quadratic polynomial whose zeroes are 𝛼2 and 𝛽2 .Let p(x) = 6𝑥2 − 5x + 1 Roots of p(x) are 𝛼 and 𝛽 So, Sum of roots = 𝛼 + 𝛽 = (−(−5))/6 = 𝟓/𝟔 And, Product of roots = 𝛼𝛽 = 𝟏/𝟔 We need to find quadratic polynomial whose zeroes are 𝛼2 and 𝛽2 . So, Required polynomial = q(x) = x2 − (Sum of Zeroes)x + Product of Zeroes = x2 − (𝛼2 + 𝛽2)x + 𝛼2 × 𝛽2 Using (a2 + b2) = (a + b)2 − 2an = x2 − [(𝛼 + 𝛽)2 − 2𝛼𝛽] x + (𝛼𝛽)2 Putting 𝛼 + 𝛽 = 5/6 & 𝛼𝛽 = 1/6 = 𝑥^2−[(5/6)^2−2 ×1/6]𝑥+(1/6)^2 = 𝑥^2−[25/36−1/3]𝑥+1/36 = 𝑥^2−[(25 − 12)/36]𝑥+1/36 = 𝒙^𝟐−[𝟏𝟑/𝟑𝟔]𝒙+𝟏/𝟑𝟔 We can multiply by 36 to make our equation cleaner = 36(𝑥^2−[13/36]𝑥+1/36) = 𝟑𝟔𝒙^𝟐−𝟏𝟑𝒙+𝟏

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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