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.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a

sure i'm up for it

step-by-step explanation: