Question

If α, β are zeroes of the polynomial 3x² + 14x – 5, then the value of `3((α + β)/(αβ))` is ______.

पर्याय

• `14/5`

• `42/5`

• `-14/5`

• `-42/5`

Answer 1

If α, β are zeroes of the polynomial 3x² + 14x – 5, then the value of `3((α + β)/(αβ))` is `underlinebb(42/5)`.

Explanation:

α, β be zeroes of the polynomial 3x² + 14x – 5.

To find, `3((α + β)/(αβ))`

We know that,

Sum of zeroes = α + β = `(-("Coefficient of"  x))/("Coefficient of"  x^2)`

⇒ `α + β = (-14)/3`   ...(1)

Product of zeroes = αβ = `"Constant term"/("Coefficient of"  x^2)`

⇒ `αβ = (-5)/3`   ...(2)

Putting value in `3((α + β)/(αβ))` from equation (1) and equation (2),

`3((α + β)/(αβ))`

= `3(((-14)/3)/((-5)/3))`

= `3((-14)/3 xx 3/(-5))`

= `3 xx 14/5`

= `42/5`