A third-degree real-coefficient polynomial function $P(x)$ with leading coefficient 1 has two of its roots as $-5$ and $2$.
If $P(x)$ has a local extremum at the point $x = 0$, what is the third root?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 7 } { 3 }$
D) $\frac { -5 } { 2 }$
E) $\frac { -10 } { 3 }$
A third-degree real-coefficient polynomial function $P(x)$ with leading coefficient 1 has two of its roots as $-5$ and $2$.

If $P(x)$ has a local extremum at the point $x = 0$, what is the third root?

A) $\frac { 1 } { 2 }$\\
B) $\frac { 3 } { 2 }$\\
C) $\frac { 7 } { 3 }$\\
D) $\frac { -5 } { 2 }$\\
E) $\frac { -10 } { 3 }$