Question

If 2 is a zero of the polynomial $p\left(x\right)=x-2kx²+kx-1$ then find value of $k$.

Answer 1

Given polynomial $p\left(x\right)=x-2kx²+kx-1$ is zero polynomial if $x$ is 2

Replace $x$ by 2 we get,

$p\left(2\right)=2-(2\times k\times 2²)+(k\times 2)-1=0$

$\Rightarrow 2-8k+2k-1=0$

$\Rightarrow 6k=1$

$\Rightarrow k=\frac{1}{6}$

Hence, value of $k$ is $\frac{1}{6}$