Post a New Question

math

posted by on .

determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)=2x^2-5x+3 at exactly one point

determine the value(s) of k such that the linear function g(x)=4x+k does not intersect the parabola f(x)=-3x^2-x+4

  • math - ,

    2x^2 - 5x + 3 = 3x + k
    2x^2 - 8x + (3-k) = 0

    We want both roots of this to be the same. That is, it must be a perfect square.

    2(x-2)^2 = 2x^2 - 8x + 8

    So, we want 3-k=8 or k=-5

    SO, 3x-5 intersects the parabola in exactly one point.

    -----------

    If the line does not intersect the parabola, then f(x)-g(x) = 0 must have a negative discriminant.

    The line intersects the parabola when

    4x+k = -3x^2 - x + 4
    3x^2 + 5x + k-4 = 0

    5^2 - 4(3)(k-4) = 25 - 12k + 48 = 73 - 12k < 0

    73-12k < 0
    k > 73/12

Answer This Question

First Name:
School Subject:
Answer:

Related Questions

More Related Questions

Post a New Question