1993 AMC 12 Question 20
AMC12 · 1993 AMC 12
Consider the equation $10z^2-3iz-k=0,$ where $z$ is a complex variable and $i^2=-1.$ Which of the following statements is true?
For all positive real numbers $k,$ both roots are pure
imaginary.
For all negative real numbers $k,$ both roots
are pure imaginary.
For all pure imaginary numbers $k,$ both roots are real and
rational.
For all pure imaginary numbers $k,$ both roots are real and
irrational.
For all complex numbers $k,$ neither root is real.