$If x^2-3ax+14=0 and x^2+2ax-16=0$ have a common root then $a^4+a^2=$

Let $\alpha$ be the common root of the equation $x^2-3ax+14=0 and x^2+2ax-16=0$

$$\begin{gathered} \Rightarrow {\alpha }^2-3a\alpha +14=0-----\left(1\right) \\ and {\alpha }^2+2a\alpha -16=0-----\left(2\right) \\ \left(1\right)-\left(2\right)\Rightarrow -5a\alpha +30=0 \\ \Rightarrow \alpha =\frac{30}{5a}=\frac{6}{a} \\ from \left(1\right) \frac{36}{a^2}-3a\left(\frac{6}{a}\right)+14=0 \\ \Rightarrow \frac{36}{a^2}=4 \\ \Rightarrow a^2=9 \\ \therefore a^4+a^2=81+9=90 \end{gathered}$$