For which values of k, does the equation x^{2}-kx+2=0 have real and distinct solutions?
- A. -2\sqrt{2} \lt k \lt 2\sqrt{2}
- B. k \lt -2\sqrt{2} only
- C. k \gt 2\sqrt{2} only
- D. k \lt -2\sqrt{2} or k \gt 2\sqrt{2} ✓
Correct Answer: D. k \lt -2\sqrt{2} or k \gt 2\sqrt{2}
Explanation
For real and distinct roots, the discriminant D \gt 0. Here, D = (-k)^2 - 4(1)(2) = k^2 - 8. Thus, k^2 - 8 \gt 0 \implies k^2 \gt 8, which means k \lt -2\sqrt{2} or k \gt 2\sqrt{2}.
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