Question

If α, β are the zeroes of the polynomial f(x) = 5x² – 7x + 1 then `1/α + 1/β = ?`

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

⇒ `α + β = 7/5` and `αβ = 1/5` 

Now, `1/α + 1/β = (α + β)/(αβ)` 

= `(7/5)/(1/5)` 

= 7