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Maths Quadratic Equations Mix Single Correct MCQ

Published on: August 14, 2026

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 real positive numbers k, both roots are pure imaginary

For real negative numbers k, both roots are pure imaginary

For all pure imaginary numbers k, both roots are real and irrational

For all complex numbers k, neither root is real

Text Solution

Verified by Experts

The correct answer is:

Use the quadratic formula to obtain

which has the discriminant, D = –9 + 40k.

If k = 1, then D = 31, so is false.

If k = i, then D = –9 + 40i = 16 + 40i – 25 = (4 + 5i) 2 ,

and the roots are and , So is false.

If k = 0(which is a complex number), then the roots are 0 and , so is false.

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