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

Advanced Math practice question

The system y = kx + 1 and y = x² + 3x + 5 has exactly one solution, and k > 0. What is the value of k?

Answer: 7

x² + (3 − k)x + 4 = 0 has one solution when (3 − k)² = 16, so 3 − k = ±4 and k = −1 or k = 7. Since k > 0, k = 7.

Common wrong answers

If you answered 3
3 is the parabola's linear coefficient.
If you answered 4
4 is the square root of 16, not k.
If you answered -1
−1 is the negative value of k.

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