​ If α and β are the zeros of the quadratic polynomial f(x) = x^2 + 5x + 4, find the value of 1/α + 1/β - 2αβ

Question

If α and β are the zeros of the quadratic polynomial f(x) = x² + 5x + 4, find the value of  \(\frac{1}{α}\) + \(\frac{1}{β}\)- 2αβ

Answer 1

Given:

α and β are the zeros of the quadratic polynomial f(x) = x² + 5x + 4

To find:

the value of \(\frac{1}{α}\) - \(\frac{1}{β}\) - 2αβ

Solution:

α and β are the roots of the given eqn.

We know,

Sum of the roots = \(\frac{-coefficient\,of\,x}{coefficient\,of\,x^2}\)

⇒ α + β = \(\frac{(-5)}{1}\) = 5

And Product of the root = \(\frac{constant\,term}{coefficient\,of\,x^2}\)

= \(\frac{4}{1}\) = 4

⇒ α x β = \(\frac{4}{1}\) = 4

Now,

On substituting values from above, we get