Solve the polynomial inequality.
-$2 x ^ { 3 } + 9 x ^ { 2 } - 38 x - 21 0$
A) $[ - 7 , - 1 / 2 ] \cup [ 3 , \infty )$
B) $( - 7 , - 1 / 2 ) \cup ( 3 , \infty )$
C) $( \infty , - 7 ] \cup [ - 1 / 2,3 ]$
D) $( \infty , - 7 ) \cup ( - 1 / 2,3 )$

Question

Solve the polynomial inequality.
-$2 x ^ { 3 } + 9 x ^ { 2 } - 38 x - 21 > 0$
A) $[ - 7 , - 1 / 2 ] \cup [ 3 , \infty )$
B) $( - 7 , - 1 / 2 ) \cup ( 3 , \infty )$
C) $( \infty , - 7 ] \cup [ - 1 / 2,3 ]$
D) $( \infty , - 7 ) \cup ( - 1 / 2,3 )$

Quizplus · Accepted Answer

To solve the inequality $2x^3 + 9x^2 - 38x - 21 > 0$, we first find the roots of the polynomial equation $2x^3 + 9x^2 - 38x - 21 = 0$. The roots divide the real number line into intervals. We then test each interval to determine where the polynomial is positive. The correct intervals where the polynomial is greater than zero are $(-7, -1/2)$ and $(3, \infty)$, indicating that the solution does not include the endpoints, hence the correct choice is B.

Solve the Polynomial Inequality 2x3+9x2−38x−21>02 x ^ { 3 } + 9 x ^ { 2 } - 38 x - 21 > 02x3+9x2−38x−21>0

Solve the Polynomial Inequality $2 x ^ { 3 } + 9 x ^ { 2 } - 38 x - 21 > 0$