Find the value of $\displaystyle a$ and $\displaystyle b$ $\displaystyle (a,b \in R)$ given that $\displaystyle 2i$ and $\displaystyle 3i$ are roots of $\displaystyle P(z)=z^{3}+aiz^{2}+bz-12i$
I don't understand how to do this.
Find the value of $\displaystyle a$ and $\displaystyle b$ $\displaystyle (a,b \in R)$ given that $\displaystyle 2i$ and $\displaystyle 3i$ are roots of $\displaystyle P(z)=z^{3}+aiz^{2}+bz-12i$
I don't understand how to do this.
Hint: If $\displaystyle \displaystyle 2i$ is a root then $\displaystyle \displaystyle P(2i) = 0$, and if $\displaystyle \displaystyle 3i$ is a root then $\displaystyle \displaystyle P(3i) = 0$.
You should end up with two equations in two unknowns ($\displaystyle \displaystyle a,b$) that you can solve simultaneously.