Question

If α and β are the zeroes of the polynomial f(x) = 5x² – 7x + 1 then find the value of `(α/β + β/α)`.

Answer 1

Since, α and β are the zeroes of the quadratic polynomial f(x) = 5x² – 7x + 1

So, `α + β = -((-7)/5) = 7/5`   ...(i)

And `αβ = 1/5`   ...(ii)

Now, `α/β + β/α = (α^2 + β^2)/(αβ)`

= `((α + β)^2 - 2aβ)/(αβ)`

= `((7/5)^2 - 2 xx 1/5)/(1/5)`   ...[From equations (i) and (ii)]

= `(49/25 - 2/5)/(1/5)`

= `((49  -  10)/25)/(1/5)`

= `(39 xx 5)/25`

= `39/5`