Find all zeros of the polynomial:
P(x)= x^4 + x^3 + 7x^2 +9x - 18

I found there is -2, and 1 as possible zeros. But how do you find plus or minus 3i

Question

Find all zeros of the polynomial:
P(x)= x^4 + x^3 + 7x^2 +9x - 18


I found there is -2, and 1 as possible zeros. But how do you find plus or minus 3i

anonymous · Answer

now that you have this roots divide the polynomial by this roots and you will get a quadratic equation.., ok?

anonymous · Answer

for exemple:  (x^4 + x^3 + 7x^2 +9x - 18)/(x-1)

anonymous · Answer

the synthetic division results from -2 and 1…?

anonymous · Answer

the roots that tou find you divide the polynomial by (x-R), R is the root that you found

anonymous · Answer

im not following.

helder_edwin · Answer

the ruffini rule (i don't know if you call this synthetic division) gives you

        1     1     7     9     -18
1             1     2     9        18
_________________________________
         1    2     9     18         0
-2          -2    0     -18
_________________________________
         1    0     9     0

so when you divide you original polynomial by (x-1)(x+2) you get x^2+9 whose roots are 3i and -3i

anonymous · Answer

that's it!, but you can use Synthetic Division too ok

anonymous · Answer

will get the same result

anonymous · Answer

okay thanks