SOLUTION: The question is: Find all the real and complex zeros of the polynomial x^4+8x^3+16x^2-8x-17 (A) 4, -4, 1 -2i, 1+2i (B) 1 -1, -4 -i, -4+i (C) none of these (D) 1, -1,

Question 31752: The question is:
Find all the real and complex zeros of the polynomial
x^4+8x^3+16x^2-8x-17
(A) 4, -4, 1 -2i, 1+2i
(B) 1 -1, -4 -i, -4+i
(C) none of these
(D) 1, -1, -4 -2i, -4+2i
This is conufusing- thanks for your help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I assume you know synthetic division.
Since the coefficients of the polynomial add up to zero
"1" is a zero of the polynomial.
Using "1" in synthetic division you find a quotient
of 1 9 25 17
Using "-1" in synthetic division you next get a quotient
of 1 8 17 or x^2 +8x + 17
This you can solve with the quadratic formula and find
zeroes at x= -4+i and -4-i
So you have zeroes at 1, -1, -4+i, and -4-i
Cheers,
stan H.
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