ANALYZING ROOTS? i really cant do this at all, PLEASE HELP!!!!!?

Question

Analyze the roots of the polynomial P(x) = x^4 + 3x^3 - 5x^2 + 2x – 4

a. Tell how many possible positive rational roots.

b. Tell how many possible negative rational roots.

c. Tell how many possible complex roots.

Answer 1

Any rational root must be a divisor of 4.
So the possible positive rational roots are 1, 2 and 4.
The possible negative rational roots are -4, -2 and -1.
So there are are 3 possible positive rational roots
and 3 possible negative rational roots.
The complex roots must occur in conjugate pairs,
i.e., if a+ bi is a complex root, so is a - bi.
So the number of possible complex roots is 0, 2 or 4.

Answer 2

As a general solution, there are as many roots of a polynomial as its degree. So, it has a total ot 4 roots. They can either all be real, all be complex or both real and complex.

Answer 3

Do you mean "rational" or "real"?

If you really meant "real", it's a problem in Descarte's Rules of Signs.