Question

If α, β are the zeroes of the polynomial 6x² − 5x − 4, then `1/alpha + 1/beta` is equal to ______.

Options

• `5/4`

• `-5/4`

• `4/5`

• `5/24`

Answer 1

If α, β are the zeroes of the polynomial 6x² − 5x − 4, then `1/alpha + 1/beta` is equal to `bbunderline(-5/4)`.

Explanation:

Given α, β are the zeroes of the polynomial P (x) = 6x² − 5x − 4

⇒ α + β = sum of zeros = `(-(-5))/6 = 5/6`

and `alpha * beta = (-4)/6 = (-2)/3`

So, `1/alpha + 1/beta = (alpha + beta)/(alpha beta)`

= `(5/6)/((-2)/3)`

= `5/6 xx 3/-2 = (-5)/4`