Question

Find all the real and imaginary zeros of the polynomial function:
f(x)=6x^3+25x^2+12x-7

Answer 1

\(x=-1\) works more or less by inspection
then you can factor out the \(x+1\) and solve the resulting quadratic.
i would do this
http://www.wolframalpha.com/input/?i=6x^3%2B25x^2%2B12x-7

Answer 2

Does this have any imaginary roots?

Answer 3

did you look at the link?

Answer 4

I did...so the only roots are -1, -7/2, 1/3?

Answer 5

yes

Answer 6

it is a polynomial of degree 3, so it can have at most 3 roots.
since there are 3 real ones there are no complex ones

Answer 7

so basically just guess and check and keep using synthetic division?