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# A simple question. (Maths) Watch

1. A line has equation y=2x-7 and a curve has equation y=x^2 - 4x+c, where c is a constant. Find the set of possible values of c for which the line does not intersect the curve.
2. X^2 - 4X + c = 2X - 7
X^2 - 6X + (c + 7) = 0
b^2 - 4ac < 0
36 - (4 x 1 )(c + 7) < 0
36 - 4c - 28 < 0
-4c + 8 < 0
-4c < -8
4c > 8
c > 2
3. (Original post by synchros)
A line has equation y=2x-7 and a curve has equation y=x^2 - 4x+c, where c is a constant. Find the set of possible values of c for which the line does not intersect the curve.
If the line and curve intersect
x^2 - 4x+c =2x-7

As it doesn't, this equation has no solutions.
Rearrange the quadratic and use the discriminant for no solutions b^2 - 4ac < 0

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Updated: April 10, 2016
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