Question

If 1 - 2i is a root of 3x2 + ax + b = 0, find the value of b.

Answer 1

We know that one root is 1-2i, and as the imaginary roots are conjugates, we obtain that the another root should be 1+2i. This means that we are able to factorize the polynomial as:

`(x-(1-2i))(x-(1+2i))=3x^2+ax+b`

And, as such, the value of b will be the multiplication of both roots (because is the coefficient without a letter). In this case,

`\begin{gathered} b=(1-2i)(1+2i) \\ =1-(2i)^2 \\ =1-4i^2 \\ =1-4(-1) \\ =1+4=5 \end{gathered}`

This means that the value of b must be 5.