$x^2-7x+12$ Where b is negative and c is positive Factored Form

Question

I have a problem in an old math book I was going over where I cant find a solution.

$x^2-7x+12$ Where B is negative and C is positive.

I cant seem to find anything that works where B is negative and C is positive.

Answer 1

Note that $(x-p)(x-q)=x^2-(p+q)x+pq: p,q\gt 0$ is a pattern for negative coefficient of $x$ and positive constant term.

Answer 2

Note that$$x^2-7x+12 = (x-3)(x-4)$$ In general if C is negative $ x^2+Bx+C =0 $ has real solutions, since in that case $B^2-4C>0$.

We can not say much for the case where $C>0.$