Determine all possible rational solutions of the polynomial equation.
$x^{3} + 15 x^{2} + 20 x + 6 = 0$
The list of all the possible rational solutions is
(Simplify your answer. Use a comma to separate answers as needed.)

Answer

Expert–verified

Hide Steps

Answer

Checking these values, we find that the rational roots are $- 1, - 2, - 3$ .

Steps

Step 1 ：By the Rational Root Theorem, the only possible rational roots are of the form $\pm \frac{a}{b}$ , where $a$ divides 6 and $b$ divides 1.

Step 2 ：Thus, the possible rational roots are $\pm 1, \pm 2, \pm 3, \pm 6.$

Step 3 ：Checking these values, we find that the rational roots are $- 1, - 2, - 3$ .