# 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,

Algebra ->  Algebra  -> College  -> Linear Algebra -> 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,      Log On

 Algebra: Linear Algebra (NOT Linear Equations) Solvers Lessons Answers archive Quiz In Depth

 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(57412)   (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.