Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } + 10 x - 23

Question

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } + 10 x - 23 < 0$$
A) $( - 5 - \sqrt { 2 } , - 5 + \sqrt { 2 } )$
B) $( 5 - \sqrt { 2 } , 5 + \sqrt { 2 } )$
C) $( -\infty , 5 - \sqrt { 2 } ) \cup ( 5 + \sqrt { 2 } , \infty )$
D) $( -\infty , - 5 - \sqrt { 2 } ) \cup ( - 5 + \sqrt { 2 } , \infty )$

Quizplus · Accepted Answer

The inequality is a quadratic inequality. The solution set is the interval between the two x-intercepts of the parabola. The x-intercepts are $x = 5 - \sqrt { 2 } $ and $x = 5 + \sqrt { 2 } $. Therefore, the solution set is $( -\infty , 5 - \sqrt { 2 } ) \cup ( 5 + \sqrt { 2 } , \infty )$.

Solve the Inequality −x2+10x−23<0- x ^ { 2 } + 10 x - 23 < 0−x2+10x−23<0

Solve the Inequality $- x ^ { 2 } + 10 x - 23 < 0$