Question

Find the roots (including the complex numbers) of the quadratic f(x)=x^2-3x+4 . Then find all complex numbers where the f(x) is a real number. Show all work to justify your answer.

Answer 1

Do you know how to solve a quadratic equation?

Answer 2

yes

Answer 3

\[x^2-3x+4=0\\ax^2+bx+c=0\\x=\frac{-b \pm \sqrt{b^2-4ac}}{2}\]
\[x=\frac{ +3 \pm \sqrt{9-16}} {2}=\frac{ +3 \pm \sqrt{-7}} {2}=\frac{3 \pm \sqrt{7}i }{2}\]