Solve the problem.
-Given $f ( x ) = x ^ { 2 } + 5 x + 6$, find all values for $x$ for which $f ( x ) 0$.
A) $( - 2 , \infty )$
B) $( - \infty , - 3 )$
C) $( - 3 , - 2 )$
D) $( - \infty , - 3 ) \cup ( - 2 , \infty )$

Question

Solve the problem.
-Given $f ( x ) = x ^ { 2 } + 5 x + 6$, find all values for $x$ for which $f ( x ) > 0$.
A) $( - 2 , \infty )$
B) $( - \infty , - 3 )$
C) $( - 3 , - 2 )$
D) $( - \infty , - 3 ) \cup ( - 2 , \infty )$

Quizplus · Accepted Answer

To find the values of $x$ for which $f(x) > 0$, we first need to find the roots of the quadratic equation $x^2 + 5x + 6 = 0$. Factoring the equation gives $(x + 3)(x + 2) = 0$, so the roots are $x = -3$ and $x = -2$. Since the leading coefficient (1) of the quadratic equation is positive, the parabola opens upwards, meaning $f(x) > 0$ outside the interval between the roots. Therefore, the correct answer is $( - \infty , - 3 ) \cup ( - 2 , \infty )$.

Solve the Problem f(x)=x2+5x+6f ( x ) = x ^ { 2 } + 5 x + 6f(x)=x2+5x+6

Solve the Problem $f ( x ) = x ^ { 2 } + 5 x + 6$