finding zeros of an equation?

Question

x^3+5x^2+10x+12

I know there are 3 zeros, and that 2 are unreal.

Answer 1

Any integer zeroes have to be factors of the constant term, which is 12 in this problem. I usually start with 1, and substitute factors of 12 (both positive and negative ) in the polynomial until I get a zero for an answer.

In this case -3 does the job. If -3 is a zero of the function, that means that (x+3) is a factor. [If x+3 = 0, then x = -3]

Divide your original polynomial by x+3. You'll get a quadratic polynomial that can be solved with quadratic formula to get the other zeroes.

If you know synthetic substitution, it goes a bit faster.

Answer 2

-27+45-30+12=0
-3 is one real root
Use horner method

1 5 10 12
-3 -3 -6 -12
--------------------------
1 2 4 0

x^2+2x+4=0

(-2+ or - sqrt(4-16))/2
are imanigary roots