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