Readonly, ID: ef$94$a$0$

Part $4$

If $a,b0,$ the cubic polynomial defined in part $3$ has a root

$r(a,b)=-a+\sqrt[3]{-q+d}+\sqrt[3]{-q-d}$

where $q=b+a^3$ and $d=\sqrt[\phantom{2}]{b^2+2a^{3}b}.$

Write a Python function $r(a,b)$ which returns $-a+\sqrt[3]{-q+d}+\sqrt[3]{-q-d}$ where $q$ and $d$ are as above.

You can assume that the inputs a and $b$ to your function will be nonnegative real numbers. It is OK to use your real$\_$cube$\_$root function if you want, and you do not need to define it again in this code cell.