Final answer:
To find all zeros of the function f(x), we observe that 1 is a zero and use polynomial division to get a quadratic equation, then apply the quadratic formula to find the remaining zeros.
Step-by-step explanation:
To find all of the zeros of the function f(x) = x^3 – 13x^2 + 392x – 27, we first note that since f(1) = 0, the number 1 is a zero of the function.
This means that (x - 1) is a factor of the polynomial.
To find the other zeros, we can divide the polynomial by (x - 1) to reduce it to a quadratic, which we can then solve either by factoring, completing the square, or using the quadratic formula.
After simplifying the polynomial upon division, we would get a quadratic equation in the form of ax^2 + bx + c = 0.
Assuming the polynomial simplifies to ax^2 + bx + c, we would use the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)]/(2a), to find the other two zeros of the polynomial.