Question

2. Find the values of k for which the line 2x + y = 2 and the curve y = (3 + sqrt(k)) * x ^ 2 - sqrt(k) * x + 6do not intersect.

Answer 1

Answer:

k > 6 or k < -2

Step-by-step explanation:

Set the y values equal to get

2x - 1 = x^2 + kx + 3

x^2 + (k - 2)x + 4 = 0.

We will get two distinct real solutions if the discriminant is greater than 0. The inequality is

(k - 2)^2 - 4(1)(4) > 0

(k - 2)^2 > 16

|k - 2| > 4

k - 2 > 4 or k - 2 < -4

k > 6 or k < -2

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