If α and β are the zeroes of the quadratic polynomial f(x) = x^2 + x – 2, find the value of 1/α – 1/β.

Question

If α and β are the zeroes of the quadratic polynomial f(x) = x² + x – 2, 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 = 1, b = 1 and c = – 2 

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

= – \(\frac{(1)}{1}\) 

= -1 

Product of the roots = αβ = \(\frac{c}{a}\)

= \(\frac{-2}{1}\) 

= – 2 

\(\frac{1}{α} – \frac{1}{β}.\)

⇒ \([\frac{(β – α)}{ αβ}]\)