Advanced MathVery hardChoosing k so a system has no solution
Advanced Math practice question
For which value of k does the system y = x² + 3 and y = k have NO solution?
- A. k = 2Correct
- B. k = 3
- C. k = 4
- D. k = 7
Answer: A. k = 2
x² + 3 is always at least 3, so y = k meets the parabola only when k ≥ 3. k = 2 gives no solution.
Why the other answers are wrong
- B. k = 3
- k = 3 touches the vertex: one solution.
- C. k = 4
- k = 4 gives x² = 1: two solutions.
- D. k = 7
- k = 7 gives x² = 4: two solutions.
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