Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. ​f(x) = 3x^4-2x^3+74x^2-50x-25

Answer 1

real zeros are x=1 and x=-1/3 found by graphing and finding the x intercepts

corresponding factors are (x-1)(x+1/3) or 3(x-1)(3x+1) = 3(3x^2 -2x-1)

divide the 4th degree poly by 3x^2 -2x -1 which gives x^2 +25 with no remainder

x^2 = -25

x= +5i and -5i the conjugate pair of imaginary solutions

complex zeros includes both real and imaginary zeros

= 5i, -5i, 1, -1/3