What do the $p$ and $q$ stand for in this quadratic formula?

Question

I study Computer Science in a German university and they use another formula to solve the quadratic equations. They call it the P-Q-Formel.

I'm used to this formula. While the Germans use this one.

Normally I'd find the values of a, b , c and D and solve the equation using the old formula but I can't seem to wrap my head around this one.

What do the p and the q stand for?

Answer 1

If we reduce $ax^2+bx+c=0$ by $a$ we get $$x^2+{b\over a}x+{c\over a}=0$$ Puting $$ p={b\over a}\;\;\;{\rm and} \;\;\;q={c\over a}$$ we get $$x^2+px+q=0$$ So $$ {-p\pm \sqrt{p^2-4q}\over 2} = {-p\over 2}\pm \sqrt{{p^2\over 4}-q}$$

Answer 2

You have $$ax^2+bx+c=0$$ after dividing by $$a\ne 0$$ you will get $$x^2+\frac{b}{a}x+\frac{c}{a}=0$$ and now let us define $$p=\frac{b}{a}$$ and $$q=\frac{c}{a}$$ and you will get $$x_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p^2}{4}-q}$$