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March 27, 2015

Posted by **Melissa** on Monday, October 24, 2011 at 4:40pm.

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 -
**Steve**, Monday, October 24, 2011 at 5:32pm2x^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.

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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

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