Find all the rational zeros of the function
$f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225$.

A) $x = - 3,5 , - 5 , - \frac { 2 } { 3 }$

B) $x = 2 , - 15,5$

C) $x = 3,5 , - 5 , \frac { 3 } { 2 }$

D) $x = - \frac { 3 } { 5 } , \frac { 5 } { 2 } , \frac { 3 } { 2 } , - 5$

E) $x = 2 , - 15 , \frac { 5 } { 2 } , \frac { 3 } { 2 }$

Question

Find all the rational zeros of the function
 $f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225$.

A) $x = - 3,5 , - 5 , - \frac { 2 } { 3 }$

B) $x = 2 , - 15,5$

C) $x = 3,5 , - 5 , \frac { 3 } { 2 }$

D) $x = - \frac { 3 } { 5 } , \frac { 5 } { 2 } , \frac { 3 } { 2 } , - 5$

E) $x = 2 , - 15 , \frac { 5 } { 2 } , \frac { 3 } { 2 }$

Quizplus · Accepted Answer

The rational zeros of the polynomial can be found using the Rational Root Theorem and testing possible candidates. The correct rational zeros are $x = 3, 5, -5, \frac{3}{2}$.

Find All the Rational Zeros of the Function f(x)=2x4−9x3−41x2+225x−225f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225f(x)=2x4−9x3−41x2+225x−225

Find All the Rational Zeros of the Function $f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225$