If α and β are the zeros of the quadratic polynomial f(x) = x^2 - x - 4, find the value of 1/α - 1/β - αβ

Question

If α and β are the zeros of the quadratic polynomial f(x) = x² - x - 4, find the value of \(\frac{1}{α}\) + \(\frac{1}{β }\) - αβ

Answer 1

Let and β are the roots of the given eqn

Sum of the roots

Product of the roots

On substituting values from above, we get

= \(\frac{-1}{4}\) + 4 = \(\frac{-1+16}{4}\)

= \(\frac{15}{4}\)