Question

What is the sum of the roots of the polynomial shown below?
ƒ(x)=x^3-8x^2-23x+30

Answer 1

look at the coefficient of the power of x to the right of the leading power of x. its the negative of that. (lol that sounds confusing)

Answer 2

The second coefficient in that polynomial is -8
so the sum of the roots is 8

Answer 3

f(1)=0 so x=1 is a zero => x-1 is a factor
1 | 1 -8 -23 30
| 1 -7 -30
---------------------
1 -7 -30 | 0
x^2-7x-30 is another factor

x^2-7x-30=(x-12)(x+5)

x=12, x=-5 our roots too

s0 1+12+(-5)=13-5=8

Answer 4

but that looks faster what joe has lol

Answer 5

i never seen this way joe

Answer 6

if you ever have a polynomial like:
\[x^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots +a_1x+a_0 = 0\]
the sum of the roots is:
\[-a_{n-1}\]
and the product of the roots is:
\[(-1)^na_0\]

Answer 7

wow i like this can we prove it?

Answer 8

Would you like to do the proof form scratch? I think i have a proof lying around on my computer cause I had to do it for a test once.

Answer 9

i'm going to watch a movie and i want to try it on my own so don't post anything k?

Answer 10

sure thing :)

Answer 11

see ya later :)