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Find the set of values of k for which the equation x^4 + kx^2 + k=0 has purely imaginary roots.

Find the set of values of k for which the equation x^4 + kx^2 + k=0 has purely imaginary roots.

Grade:11

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Put x^2 = m
m^2 + km + k = 0

for purely imaginary roots,
Discriminant,D = (b^2 –4ac)< 0
D = k^2 –4k < 0
k(k-4) < 0
K belongs to (0,4)

Thanks

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