Question

What are the roots of 2x+5/x=2
express in a+bi form

Answer 1

multiply all by x:
2x^2+5=2x
set equal to zero:
2x^2-2x+5=0
solve using the quadratic formula using a=2, b=-2, c=5:
\[x=(-b \pm \sqrt{b^2-4ac})/2a=(2 \pm \sqrt{2^2-4(2)(5)})/2(2)\]\[=(2 \pm \sqrt{4-40})/4=(2 \pm \sqrt{-36} )/4=(2 \pm 6i)/4\]\[=1/2 \pm (3/2)i\]