Answer
The statement is true.
Work Step by Step
The given inequality, from Exercise 1, is ${{x}^{2}}+8x+15>0$ >. Solving the equation $f\left( x \right)={{x}^{2}}+8x+15=0$ , the boundary points obtained are $x=-5,-3$.
That is, the points, -5 and -3, are the roots of the function and on these values the function changes from positive to negative or negative to positive. Then, the interval is divided into three intervals as $\left( -\infty ,-5 \right),\left( -5,-3 \right)\text{, and }\left( -3,\infty \right)$.
Now, the rightmost interval is $\left( -3,\infty \right)$. Thus, any value in this interval can be chosen as the test value for the function and 0 lies in this interval.
Thus, 0 can be used as a test value. Hence, the given statement is true.
