State how many imaginary and real zeros the function has. f(x) = x4 - 8x3+ 17x2- 8x +16

First of all, we don't have a formula for solving polynomials with degree 4. We can try to use the rational root theorem, which states that if this polynomial has a rational root, it must be a divisor of 16.

So, we have to try

You will see that 4 is a root. So, we can divide

We can repeat the process, and check all the divisors of -4, i.e.

You'll see that 4 is again a root, and we have

Now we have a quadratic polynomial which we can simply solve:

So, the roots of this polynomials are 4 (twice), i and -i.

the 4th choice is the correct one

step-by-step explanation:

i can you with this answer

step-by-step explanation: