Question

If α and β are the zeros of the polynomial f(x) = 6x² + x – 2, find the value of  `(α/β + α/β)`.

Answer 1

By using the relationship between the zeroes of the quadratic polynomial.

We have 

Sum of zeroes = `(-("Coefficient of"  x))/("Coefficient of"  x^2)` and Product of zeroes = `"Constant term"/("Coefficient of"  x^2)` 

∴ `α + β = -1/6` and `αβ = -1/3` 

Now, `α/β + β/α = (α^2 + β^2)/(αβ)`

= `(α^2 + β^2 + 2αβ - 2αβ)/(αβ)` 

= `((α + β)^2 - 2αβ)/(αβ)` 

= `((-1/6)^2 - 2(-1/3))/(-1/3)` 

= `(1/36 + 2/3)/(-1/3)`   

= `-25/12`