​ If α and β are the zeros of the quadratic polynomial p(y) = 5y^2 - 7y + 1, find the value of 1/α + 1/ β ​

Question

If α and β are the zeros of the quadratic polynomial p(y) = 5y² - 7y + 1, find the value of \(\frac{1}{ α}\)+ \(\frac{1}{β}\) 

Answer 1

Let α and β are the roots of the given eqn

Sum of the roots =  α + β

= \(\cfrac{-coefficient\,of\,x}{coefficient\,of\,x^2}\) = - \(\frac{(-7)}{5}\) = \(\frac{7}{5}\)

Product of the roots =  α x β

= \(\cfrac{constant\,term}{coefficient\,of\,x^2}\) = \(\frac{1}{5}\)

On substituting values from above, we get