Answer to Question #181156 in Algebra for will

Question

List the possible roots using the Rational Root Theorem

f(x)= 2x³ - 3x² - 3x + 2

Answer 1

If there is a rational root $p/q$ then $q$ must divide $a_n$ and $p$ must divide $a_0$.

So, divisors of $a_n=2$: {-1, -2, 2, 1}

Divisors of $a_0 =2$ : {-1, -2, 2, 1}.

Thus, if any rational roots exist, they must have a denominator of 1 or 2 and a numerator of 1or 2, which limits the choices to $1/2$ and 1 and their corresponding negative values.

So, possible roots are {-1, -1/2, 1/2, 1}.

Answer: ${-1, -1/2, 1/2, 1}.$