If α and β are the zeros of the quadratic polynomial p(y) = 5y2 –

1.	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» 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

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»

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