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 ${\displaystyle \alpha }$, ${\displaystyle \beta }$ be the zeros of the polynomial ${\displaystyle f\left(x\right)=2x^3-3k{x}^2+4x-5}$ and we are given tha 

${\displaystyle \alpha +\beta +\gamma =6}$

Then,

${\displaystyle \alpha +\beta +\gamma =6}$

${\displaystyle \alpha +ß+\gamma =-\frac{\text{coefficient of x}}{\text{coefficient of}{x}^2}}$

${\displaystyle =-\frac{-3k}{2}=\frac{3k}{2}}$

Substituting ${\displaystyle \alpha +\beta +\gamma =\frac{3k}{2}}$ , we get

${\displaystyle \frac{+3k}{2}=6}$

${\displaystyle +3k=12}$

${\displaystyle k=\frac{12}{+3}}$

${\displaystyle k=+4}$

The value of k is 4 ,

Hence, the correct alternative is ${\displaystyle \left(b\right)}$