Show that $\dfrac{b}{a} = -(A+B+C)$ and $\dfrac{c}{a} = (AB+AC + BC)$

Question

Let´s assume we have the polynomial: $ax^3+bx^2+cx+d$

This polynomial has three zero points: $A$, $B$ and $C$.

How can I show that $$\dfrac{b}{a} = -(A+B+C)$$

and

$$\dfrac{c}{a} = (AB + AC + BC)$$?

Thanks for your help!

Answer 1

HINT: note that if $A,B,C$ are the zero points of $$ax^3+bx^2+cx+d$$ then you can write $$ax^3+bx^2+cx+d=a(x-A)(x-B)(x-C)$$ so $b=-a(A+B+C)$ etc.