Question

if the sum of the zeros of the polynomial f(x)=2xcube-3kx^+4x-5 then find the value of k​

Answer 1

$\underline\purple{\underline{\sf{\maltese\: Given\::-}}}$

$\red\rightarrow$ $\tt{f(x) = {2x}^{3} - 3k{x}^{2} +4x-5}$

$\underline\purple{\underline{\sf{\maltese\: To\:find\::-}}}$

$\red\rightarrow$the value of k.

$\underline\purple{\underline{\sf{\maltese\: Solution\::-}}}$

$\green\implies$ $\tt\red\boxed{ Sum\: of\:roots = \alpha + \beta + \gamma = \frac{ - b}{a}}$

$\tt{Here, b = -3 \:and\: a = 2.}$

$\green\implies$ $\tt{ Sum\: of\: roots = \frac{3k}{2}}$

$\green\implies$$\tt{\frac{3k}{2}=6}$

$\green\implies$$\tt{3k=6\times2}$

$\green\implies$ $\tt{k= \frac{12}{3}}$

∴ k = 4

$\rm\bold\blue{Hope\:it\:helps\: :)}$