Question

α, β are zeroes of the polynomial 2x² + 5x + 1. The value of `(1/α + 1/β)` is ______.

Options

• `-5/4`

• 5

• `5/4`

• –5

Answer 1

α, β are zeroes of the polynomial 2x² + 5x + 1. The value of `(1/α + 1/β)` is – 5.

Explanation:

If α, β are zeroes of the polynomial 2x² + 5x + 1, then a = 2, b = 5, c = 1

`α + β = (-b)/a`

= `(-5)/2`

And `αβ = c/a`

= `1/2`

The value of `(1/α + 1/β)`:

⇒ `1/α + 1/β`

= `(α + β)/(αβ)`

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

= `(-5)/2 xx 2/1`

= –5