# How to find the zeros of this function

• Sep 17th 2009, 07:55 AM
tsmith
How to find the zeros of this function
Find all the zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^3 + 11x^2 + 39x + 29.

So I think that I might need to use synthetic division, but I'm not sure. The teacher didn't explian this to me. Any help?
:)
• Sep 17th 2009, 08:03 AM
Quote:

Originally Posted by tsmith
Find all the zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^3 + 11x^2 + 39x + 29.

So I think that I might need to use synthetic division, but I'm not sure. The teacher didn't explian this to me. Any help?
:)

HI

Factorise f(x) , do you know how ?

\$\displaystyle f(x)=(x+1)(x^2+10x+29)\$

\$\displaystyle x^2+10x+29\$ is complex , you can always check its discriminant .

\$\displaystyle x+1\$ is a factor because \$\displaystyle f(-1)=0 \$

Then you can do the long division to get its quadratic factor .

So the zero of this polynomial would be -1 because -1 makes \$\displaystyle f(x)=0 \$
• Sep 17th 2009, 04:18 PM
pacman
[I]factor: x^3 + 11x^2 + 39x + 29 = (x + 1)(x^2 + 10x + 29) = (x + 1)(x + (5 - 2i))(x + (5 + 2i))