Question 27 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

If α,β are zeroes of quadratic polynomial 5x^2+5x+1, find the value of

1. α^2+β^2

2. α^(-1)+β^(-1)

Next: Question 28 (Choice 1) Important → Go Ad-free

Transcript

Since 𝛼 and 𝛽 are roots of 5𝑥^2+5𝑥+1 Sum of zeroes 𝛼 + 𝛽 = (− (5))/5 𝜶 + 𝜷 = −1 Product of zeroes 𝛼𝛽= 1/5 𝜶𝜷 = 𝟏/𝟓 Finding 𝜶^𝟐+𝜷^𝟐 Since 〖(𝛼" + " 𝛽)〗^2 = 𝛼^2+𝛽^2 + 2𝛼𝛽 𝜶^𝟐+𝜷^𝟐 = 〖(𝜶" + " 𝜷)〗^𝟐 − 𝟐𝜶𝜷 Substituting values from (1) and (2) 〖 𝛼〗^2+ 𝛽^2 = 〖(−1)〗^2 − 2 × 1/5 〖 𝛼〗^2+ 𝛽^2 = 1 − 2/5 〖 𝛼〗^2+ 𝛽^2 = (5 − 2)/5 𝜶^𝟐+𝜷^𝟐 = 𝟑/𝟓 Finding 𝜶^(−𝟏)+𝜷^(−𝟏) 𝛼^(−1)+𝛽^(−1) = 𝟏/𝜶 + 𝟏/𝜷 = (𝜷 + 𝜶)/𝜶𝜷 = (−1)/(1/5) = -1 × 5/1 = −5

Made by

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

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular