If x² + kx + 4 = 0 has roots differing by 2, then k equals?
- -2√5
- 2√5
- Both A and B
- None of these
Explanation
Let roots be r and r+2, since they differ by 2.
For x² + kx + 4 = 0:
1. Sum of roots = -b/a = -k → r + (r+2) = 2r + 2 = -k → r = (-k-2)/2
2. Product of roots = c/a = 4 → r(r+2) = 4
Plug r in: [(-k-2)/2] × [(-k-2)/2 + 2] = 4
→ [(-k-2)/2] × [(2-k)/2] = 4
→ (-k-2)(2-k) = 16
Simplify: k² - 4 = 16 → k² = 20 → k = ±2√5
So k can be 2√5 or -2√5.
Last verified 09-06-2026
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