We have given a quadratic polynomial f(x)=5x²-7x+1 and α and β are the zeroes of the given polynomial and we have to find the value of (1/α+1/β).
This question is taken from polynomials and it is very important for examination as it was already asked in previous year papers
Please give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2C, question no 23
Given : α and β are zeroes of f(x)=5x²−7x+1
To find : 1/α+1/β
α+β = sum of zeros = –(coefficient of x)/(coefficient of x²) =7/5
αβ = product of zeroes =( constant term)/(coefficient of x² =1/5
Now,
1/α+1/β=αβ(α+β)
=7/5×5/1
=7