Answer
a) If $c>0$, then p and q have the same sign (both are negative or both are positive)
b) Thus if $c<0$ then either p or q but not both are negative.
Work Step by Step
We known that if we simplify, we get
$$(x+q)(x+p) = x^2 +(p+q)x + pq$$
We can match the coefficients,
$$x^2+bx+c = x^2 +(p+q)x + pq$$
$$c=pq$$
If follows that if $c>0$, then p and q have the same sign (both are negative or both are positive)
Thus if $c<0$ then either p or q but not both are negative.
