Question

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

Answer 1

Given the equation:

`3x^2+ax+b=0`

Divide the equation by 3, to make the coefficient of x = 1

so,

`x^2+(a)/(3)x+(b)/(3)=0`

Given: 1 - 2i is a root of the equation

Note: the root is a complex number, while (b/3) is a real number

So, the other toot will be conjugate to the given root

so,

`\begin{gathered} (b)/(3)=(1-2i)\cdot(1+2i)=1-4i^2=1-4\cdot(-1)=1+4=5 \\ b=5\cdot3=15 \end{gathered}`

so, the value of b = 15