Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

*product

Answer 6

I had forgotten all of that, thanks satellite.

Answer 7

yw