The given statement is:

"$x=2\:\:and\:\:x=3$ are the roots of the equation $3x^2-x-10=0$."

the connecting word is 'and'.

The components are:

$p:$ "$x=2\:$ is a roots of the equation $3x^2-x-10=0$."

$q:$ "$x=3\:$ is a roots of the equation $3x^2-x-10=0$."