Solve the inequality and write the solution set in interval notation. $5 x ^ { 3 } - 20 x ^ { 2 } 0$
A) $( 4 , \infty )$
B) $( - 4 , - \infty )$
C) $( - 4 , \infty )$
D) $( 4 , - \infty )$
E) $( - \infty , 5 )$

Question

Solve the inequality and write the solution set in interval notation.​ $5 x ^ { 3 } - 20 x ^ { 2 } > 0$ ​
A) $( 4 , \infty )$
B) $( - 4 , - \infty )$
C) $( - 4 , \infty )$
D) $( 4 , - \infty )$
E) $( - \infty , 5 )$

Quizplus · Accepted Answer

First, factor the inequality: $5x^3 - 20x^2 > 0$ becomes $5x^2(x - 4) > 0$. The roots are $x = 0$ and $x = 4$. Since the inequality is greater than zero, we are looking for values of $x$ where the expression is positive. Testing intervals around the roots, we find that the expression is positive for $x > 4$, which corresponds to the interval notation $(4, \infty)$.

Solve the Inequality and Write the Solution Set in Interval 5x3−20x2>05 x ^ { 3 } - 20 x ^ { 2 } > 05x3−20x2>0

Solve the Inequality and Write the Solution Set in Interval $5 x ^ { 3 } - 20 x ^ { 2 } > 0$