I know about quadratic polynomial that $$\alpha +\beta =-\frac{b}{a}$$where $\alpha ,\beta $ are roots of the polynomial $ax^2+bx+c$
I also know it about cubic polynomial that $$\alpha+\beta+\gamma = -\frac{b}{a}$$where $\alpha,\beta,\gamma$ are roots of the polynomial $ax^3+bx^2+cx+d$
I can prove it for quadratic polynomial because I know how to calculate roots of the polynomial in terms of $a,b,c$, by quadratic formula
But I can't do it for cubic polynomial because I am afraid of the horror "cubic formula"
Also it will become more terrible when we talk about general polynomial of $n$ degree
I googled for proof of it but didn't got sufficient results
So please help me to prove the relationship between coefficients and roots of the cubic polynomial and further for general polynomial.