Question

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

Answer 1

2x² – 7x + 5 = `x^2 - 7/2x + 5/2` = 0

α + β = `7/2`

αβ = `5/2`

`alpha/beta + beta/alpha = (alpha^2 + beta^2)/(alphabeta)`

= `((alpha + beta)^2 - 2alphabeta)/(alphabeta)`

= `(alpha + beta)^2/(alphabeta) - 2`

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

= `49/4 xx 2/5 - 2`

= `49/10 - 2`

= `(49 - 20)/10`

= `29/10`