Answer
$S$ is linearly independent set of vectors.
Work Step by Step
Consider the combination
$$a(2-x)+b(2x-x^2)+c(6-5x+x^2)=0, \quad a,b,c\in R.$$
Which yields the following system of equations
\begin{align*}
2a-6c&=0\\
-a+2b-5c&=0\\
-b+c&=0.
\end{align*}
The determinant of the coefficient matrix is given by
$$\left| \begin {array}{cccc} 2&0&-6\\ -1&2&-5\\0&-1&1\end {array}
\right|=-12 $$
Since determinant is non zero, hence there exist a unique solution for the above system; that is, the trivial solution,
$$a=0,\quad b=0, \quad c=0.$$
Then, $S$ is linearly independent set of vectors.