Question

Use the Fundamental Theorem of Algebra to determine the total number of zeros of f(x)=x^3-12x^2+28x-9

Answer 1

the fundamental theorem of algebra says that a polynomial of degree n has n zeros, counting multiplicity
of course they don't all have to be real, they can be complex

Answer 2

that means your polynomial has three zeros, could be three real zeros, or one real zero and two complex zeros

Answer 3

in fact your as three real zeros, it factors as \[(x-9) (x^2-3 x+1)\]so one zero is 9, the other two are what you get if you set \(x^2-3x+1=0\) and solve for \(x\)

Answer 4

yes

Answer 5

three real zeros

Answer 6

oops deleted your comment by mistake
yes, it has 3 zeros

Answer 7

Then it says find the constant, that would be -9?

Answer 8

yes

Answer 9

And coefficient of largest power would be 1?

Answer 10

yes

Answer 11

Now how would you find the factors of p and q?

Answer 12

@satellite73