Find all complex zeros of a polynomial function. Give the exact values. List multiple zeros as necessary.

Question

f(x)=2x⁵+11x⁴+17x³+21x²+45x

Answer 1

First factor x from the given polynomial to get 2x⁴ +11x³ +17x² +21x +45. 45 is made up of 3,15 and 5,9. Choose 3 as a root and the factor becomes x+3 which when divided into the polynomial gives 2x³ +5x² +2x +15. 15 is made up of 3,5 choose 3 so that the factor is x+3 and divide it into the cubic which gives 2x² -x +5. Solve this using the quadratic formula which gives x=(1+i√39)/4 and x=(1-i√39)/4. So the five roots are x=0,-3,-3, (1+i√39)/4 and (1-i√39)/4.