Solve the problem.
-Given $f ( x ) = x ^ { 2 } - 2 x - 24$, find all values for $x$ for which $f ( x )

Question

Solve the problem.
-Given $f ( x ) = x ^ { 2 } - 2 x - 24$, find all values for $x$ for which $f ( x ) < 0$.
A) $( - \infty , - 4 ) \cup ( 6 , \infty )$
B) $( 6 , \infty )$
C) $( - \infty , - 4 )$
D) $( - 4,6 )$

Quizplus · Accepted Answer

To find the values of $x$ for which $f(x) < 0$, we first solve $f(x) = 0$. Factoring $f(x) = x^2 - 2x - 24$, we get $(x - 6)(x + 4) = 0$, so $x = 6$ or $x = -4$. The parabola opens upwards (since the coefficient of $x^2$ is positive), meaning $f(x) < 0$ between the roots. Thus, the correct interval is $(-4, 6)$.

Solve the Problem f(x)=x2−2x−24f ( x ) = x ^ { 2 } - 2 x - 24f(x)=x2−2x−24

Solve the Problem $f ( x ) = x ^ { 2 } - 2 x - 24$