1993 AHSME Problems/Problem 20

Problem

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?

$\text{(A) For all positive real numbers k, both roots are pure imaginary} \quad\\ \text{(B) For all negative real numbers k, both roots are pure imaginary} \quad\\ \text{(C) For all pure imaginary numbers k, both roots are real and rational} \quad\\ \text{(D) For all pure imaginary numbers k, both roots are real and irrational} \quad\\ \text{(E) For all complex numbers k, neither root is real}$

Solution

$\fbox{A}$

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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1993 AHSME Problems/Problem 20

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