## Algebra 1: Common Core (15th Edition)

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.
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.