Question

If the sum of the zeros of the polynomial f(x) = 2x³ − 3kx² + 4x − 5 is 6, then the value ofk is

Options

• 2

• 4

•  −2

• −4

Answer 1

Let `alpha`, `beta` be the zeros of the polynomial `f(x)= 2x^3 - 3kx^2 + 4x - 5` and we are given tha 

`alpha + beta + γ = 6`

Then,

`alpha + beta + γ = 6`

`alpha + ß + γ = - (text{coefficient of x})/(text{coefficient of } x^2)`

`= -(-3k)/2 = (3k)/2`

Substituting `alpha + beta + γ = (3k)/2` , we get

`(+ 3k )/2=6`

`+ 3k =12`

`k = 12/(+3)`

`k = + 4`

The value of k is 4 ,

Hence, the correct alternative is `(b)`