Question

Find a quadratic equation in standard form given its roots are 2+/- i square root of 3/2

Answer 1

We want to find a quadratic equation with the following roots:

`\begin{gathered} x_+=2+i\sqrt{(3)/(2)} \\ x_-=2-i\sqrt{(3)/(2)} \end{gathered}`

Then we have:

`\begin{gathered} y=(x-x_+)\cdot(x-x_-) \\ y=(x-2-i\sqrt{(3)/(2)})\cdot(x-2+i\sqrt{(3)/(2)}) \\ y=x^2-2x+i\sqrt{(3)/(2)}x-2x+4-i2\sqrt{(3)/(2)}-i\sqrt{(3)/(2)}x+i2\sqrt{(3)/(2)}+(3)/(2) \\ y=x^2-4x+(11)/(2) \end{gathered}`