Question

Use the rational root theorem to determine the list of all possible rational solutions.

 

y = x 3 + 2 x 2 + 5 x + 5

 

Answer 1

Use the rational root theorem to determine the list of all possible rational solutions.

 

$y = x ^3 + 2 x ^2 + 5 x + 5$

Rational Roots : $\pm($ factors of a_o/ factors of a_n)

a_o=5

factors of 5: 1, 5

a_n = 1

factors of 1= 1

therefore, all possible rational solutions are $\pm({1 \over 1},{5 \over 1})$

substituting the following values into the equation above, None will give zero

therefore, the equation doesn't have a rational solution