Today in highschool we were doing a chapter called "Roots of polynomials" where we learnt something new and interesting which is :
$ax^2+bx+c=0$ Has roots $\alpha$ , $\beta$ Then:
$$\alpha + \beta= -b/a$$
$$\alpha \beta=c/a$$
$ax^3+bx^2+cx+ d=0$ Has roots $\alpha$ , $\beta$ , $\gamma$. Then:
$$\alpha+ \beta + \gamma = -b/a$$
$$\alpha \beta + \alpha \gamma + \beta \gamma= c/a$$
$$\alpha \beta \gamma= -d/a$$
My curiosity turned to, what happens in 4th degree power polynomial. We haven't learnt in class (not in our syllabus). But is there something like a general formula for this? Coz I'm sure people who learn higher powers cannot memorise all the powers and remember when it becomes - or +. (For me I can memorize these because It's only a few set of equations and two different polynomials), what happens in higher powers and how does one memorise ? What is the general formula, if there is any?
And also : what happen in fourth power that is for :
$$ax^4+bx^3+cx^2+dx+e=0$$
After looking at the first comment I understood that it's Vietas formulas. And I checked in out in Wikipedia. The formulas are complicated looking, but I understood after looking for a while. But there are dots in the middle which means more equations. I tried this with my 3rd power and it works fine, but the question remains "How to do for higher degree polynomials. I don't know what are the formulas in the middle (the dots going downwards in the middle). I believe there are n number of formulas for n powers, here there is only three. Which I already knew, please help me