Pregunta
Using the rational root theorem, list out all possible/candidate rational roots of
. Express your answer as integers or as fractions in simplest
form. Use commas to separate.
form. Use commas to separate.
Ask by Evans Wilson. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The possible rational roots are: -2, -1, -1/2, -1/3, -2/3, -1/6, 1/6, 1/3, 2/3, 1/2, 1, 2
Solución

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Como
The Deep Dive
To apply the rational root theorem, we first need to identify the coefficients of the polynomial
. The potential rational roots are given by the formula
, where
is a factor of the constant term (-2) and
is a factor of the leading coefficient (6).
The factors of -2 are: ±1, ±2
The factors of 6 are: ±1, ±2, ±3, ±6
The factors of 6 are: ±1, ±2, ±3, ±6
Now we list all combinations of
:
- From
: → 1, 0.5, 0.333…, 0.1666… - From
: → -1, -0.5, -0.333…, -0.1666… - From
: → 2, 1, 0.666…, 0.333… - From
: → -2, -1, -0.666…, -0.333…
After simplifying, the rational candidate roots we get are:
±1, ±2, ±1/2, ±1/3, ±1/6, ±1/2
±1, ±2, ±1/2, ±1/3, ±1/6, ±1/2
So, the complete list of possible rational roots is:
1, -1, 2, -2, 0.5, -0.5, 0.333…, -0.333…, 0.1666…, -0.1666…
1, -1, 2, -2, 0.5, -0.5, 0.333…, -0.333…, 0.1666…, -0.1666…
Expressed in a more standard format that avoids decimals while retaining simplicity:
1, -1, 2, -2, 1/2, -1/2, 1/3, -1/3, 1/6, -1/6.
1, -1, 2, -2, 1/2, -1/2, 1/3, -1/3, 1/6, -1/6.
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