Question

State how many imaginary and real zeros the function has.

f(x) = x3 + 5x2 - 28x - 32

1 imaginary; 2 real

2 imaginary; 1 real

0 imaginary; 3 real

3 imaginary; 0 real

Answer 1

Is the answer 3 imaginarys 0 reals

Answer 2

if you factor this completely, you get (x+8)*(x-4)*(x+1) = 0

Answer 3

this means that the zeros are

-8
4
-1

so you have 3 real zeros, 0 imaginary zeros

Answer 4

Now what about this;
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

8, -14, and 3 + 9i

f(x) = x4 - 11x3 + 72x2 - 606x + 10,080

f(x) = x4 - 303x2 + 1212x - 10,080

f(x) = x4 - 11x3 - 72x2 + 606x - 10,080

f(x) = x4 - 58x2 + 1212x - 10,080

Answer 5

The rational roots theorem and some trivial analysis shows that -1 is a root.
The first pair of coefficients and the last pair differ by the same amount (4).
That means that (x+1) is a factor of the polynomial.
Make that division. The result is a quadratic, to which you can apply the quadratic formula and finish the problem.

Answer 6

still have no idea what that means