Finding real numbers of a complex polynomial

**Cthul** · January 13th 2011, 08:41 PM

Find the value of $a$ and $b$ $(a,b \in R)$ given that $2i$ and $3i$ are roots of $P(z)=z^{3}+aiz^{2}+bz-12i$

I don't understand how to do this.

**Prove It** · January 13th 2011, 08:53 PM

Hint: If $\displaystyle 2i$ is a root then $\displaystyle P(2i) = 0$ , and if $\displaystyle 3i$ is a root then $\displaystyle P(3i) = 0$ .

You should end up with two equations in two unknowns ( $\displaystyle a,b$ ) that you can solve simultaneously.

**Cthul** · January 13th 2011, 09:05 PM

How stupid of me. Thank you.

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