Question

according to the rational root theorem, which of the following are possible rational roots of, select those that apply.
3x^3+2x^2+x-4?
1. -2/3 2. -3/4 3. 1/3 4. 1/4

Answer 1

well... according to the "rational root test" or theorem.... what would be the P and Q in this expression?

Answer 2

If given a polynomial\[a _{n}x ^{n}+a _{n -1}x ^{n -1}+a _{n -2}x ^{n -2}+...+a _{1}x +a _{0}\]Then the possible rational roots are comprised of \[\frac{ factors(a _{0}) }{ factors(a _{n}) }\]

Answer 3

In your example, factors of the constant 4 are {1, 2, 4} and the factors of the leading coefficient 3 are {1, 3}. Hence the possible rational roots would be
{1, -1, 1/3, -1/3, 2/3, -2/3, 4, -4, 4/3, -4/3}

Answer 4

So 1. and 3.