Final answer:
To find the zeros of the polynomial function, we can use the quadratic formula or factor the polynomial.
Step-by-step explanation:
To find the zeros of the polynomial function f(x) = x⁴+62x²+128x+65, we need to solve the equation f(x) = 0. We can do this by factoring or by using the quadratic formula.
Since the given equation is a fourth degree polynomial, we can use the fact that a polynomial of degree n can have at most n real zeros. So in this case, there may be up to 4 real zeros.
However, factoring the given polynomial might not be easy, so we can use the quadratic formula to find the zeros. Plugging in the values a = 1, b = 62, and c = 65 into the quadratic formula and simplifying, we can find the zeros.