`P=0⇔4x^3-9x=0`
`⇒x(4x^2-9)=0`
\(⇒\left[ \begin{array}{l}x=0\\4x^2-9=0\end{array} \right.\)
\(⇒\left[ \begin{array}{l}x=0\\4x^2=9\end{array} \right.\)
\(⇒\left[ \begin{array}{l}x=0\\x^2=\dfrac94\end{array} \right.\)
\(⇒\left[ \begin{array}{l}x=0\\x=±\dfrac32\end{array} \right.\)
\(⇒\left[ \begin{array}{l}x=0\\x=\dfrac32\\x=\dfrac{-3}2\end{array} \right.\)
Vậy `P=0` khi `x∈{0;3/2;{-3}/2}`