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

From the question, it’s given that: 

α and β are the roots of the quadratic polynomial f(x) where a =5, b = -7 and c = 1 

Sum of the roots = α+β = \(\frac{-b}{a}\)

= – \(\frac{(-7)}{5}\) 

= \(\frac{7}{5}\) 

Product of the roots = αβ 

= \(\frac{c}{a}\) 

= \(\frac{1}{5}\) 

\(\frac{1}{α} +\frac{1}{β}\) 

⇒ \(\frac{(α +β)}{ αβ}\)

⇒ \(\frac{7}{5} \over \frac{1}{5}\)

= 7