The quadratic equation x² – 2kx + k² – 1 = 0 has real roots for?
- k > 1
- k < 0
- All real k
- None of these
Explanation
For real roots, discriminant D ≥ 0
Given: x² – 2kx + k² – 1 = 0
Here a=1, b=-2k, c=k² - 1
D = b² − 4ac = (-2k)² − 4(1)(k² − 1)
D = 4k² − 4k² + 4 = 4
D = 4 > 0 for every k.
Since D is always positive, roots are real and unequal for all real k.
Last verified on 09-06-2026
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