anonymous 4 years ago What is the sum of the roots of the polynomial shown below? f(x)=3x^3+12x^2+3x-18

1. agreene

set the equation equal to 0 to find the roots, you should find x= -3, -2, 1 are the roots sum (add) the roots: (-3)+(-2)+1= -4

2. anonymous

you can also do this without finding the roots (in case they are harder to find than here)

3. anonymous

if you have $ax^3+bx^2+cx+d=0$ sum of the roots is $-\frac{b}{a}$ and here you see that $-\frac{b}{a}=-\frac{12}{3}=-4$

4. anonymous

produce of the roots (not that you asked) is $-\frac{d}{a}$ in case you need that one. if all you need is product and sum, you do not need to find the roots, and in some cases finding the roots may be very hard

5. anonymous

*product

6. agreene

I had forgotten all of that, thanks satellite.

7. anonymous

yw