Question

The roots of the equation 2x² – 7x + 5 = 0 are α and β. Without solving for the roots, find `1/alpha + 1/beta`

Answer 1

2x² – 7x + 5 = `x^2 - 7/2x + 5/2` = 0

α + β = `7/2`

αβ = `5/2`

`1/alpha + 1/beta = (beta + alpha)/(alphabeta)`

= `(7/2)/(5/2)`

= `7/5`