16Hit1600
Advanced MathVery hardConstant for a line tangent to a parabola

Advanced Math practice question

The system y = x² + k and y = 2x, where k is a constant, has exactly one solution. What is the value of k?

Answer: 1

x² + k = 2x gives x² − 2x + k = 0. One solution needs discriminant 4 − 4k = 0, so k = 1.

Common wrong answers

If you answered 0
0 gives x² − 2x = 0 with two solutions, x = 0 and x = 2.
If you answered 2
2 gives a negative discriminant and no solution.
If you answered -1
−1 gives two solutions.

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