Question

Please help!! List all of the potential rational zeros of the polynomial function. Do not attempt to find the zeros. f(x)=3x^3+4x^2+x-6.

Answer 1

These are the choices:

Answer 2

@satellite73

Answer 3

@dan815

Answer 4

Any help would be really appreciated!

Answer 5

@shaik0124

Answer 6

Suggested Attack to Finding Zeros of a Polynomial

Identify the total number of real or complex zeros (corollary to Fundamental Theorem of Algebra).
Identify the possible number of positive, negative, and complex zeros (Descartes' Rule of Signs).
List the possible rational zeros (Rational Root Theorem)
Try possible rational zeros until you find one that works. After each division by a positive value, check for possible upper bounds. After each division by a negative value, check for possible lower bounds (Upper and Lower Bound Theorems)
After you find a possible rational root that actually works, take the quotient and continue to try to factor it until it is down to a quadratic or less. Once it is a quadratic or less, there are other ways to solve it.
Write the linear and or linear / irreducible quadratic factorization (next section)

Answer 7

since the question specifically mentioned "Do not attempt to find the zeros" I would assume the expected solution is to try putting the list of x values in the eqn n see which set yields zero for f(x).

Answer 8

Thank you both! =)

Answer 9

Welcome :)