Final answer:
To find the zeros of the function f(x) = 2x^3 - 12x^2 + 26x - 20 algebraically, divide f(x) by (x - 2) to obtain 2x^2 - 8x + 10. Use the quadratic formula to find the zeros of this quadratic equation: x = 2 + i√6 and x = 2 - i√6.
Step-by-step explanation:
To find the zeros of the function f(x) = 2x^3 - 12x^2 + 26x - 20 algebraically, we need to find the values of x that make the function equal to zero. Since we know that x - 2 is a factor of f(x), we can use synthetic division or polynomial long division to divide f(x) by (x - 2). By performing this division, we find that the quotient is 2x^2 - 8x + 10. To find the zeros of this quadratic equation, we can use the quadratic formula (x = (-b ± sqrt(b^2 - 4ac))/(2a)). Substituting the values of a, b, and c from the quadratic equation, we get two complex solutions: x = 2 + i√6 and x = 2 - i√6.