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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. (Original post by Revision 99)
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.
Knowing that they never intersect, how can you use quadratic equations to solve this question?
3. (Original post by SeanFM)
Knowing that they never intersect, how can you use quadratic equations to solve this question?
Okay, but then how are we supposed to solve, atleast give a starting point with an explanation
4. (Original post by Revision 99)
Okay, but then how are we supposed to solve, atleast give a starting point with an explanation
When you have the equation of the curve, are you sure it was y=x, not perhaps y=x^2
5. (Original post by Revision 99)
Okay, but then how are we supposed to solve, atleast give a starting point with an explanation
That was one, I think encouraging people to think for themselves and giving subtle prompts makes them learn the most from the question

If two curves intersect, what can you say about the curve that you get when you take one away from the other? (Think about the points of intersection originally, then what happens when you take one away from the other, specifically at the points of intersection)

Then think about what happens when they never intersect and how you can use quadratic equations to solve your question using the equation f(x) - g(x), where f and g are the two original equations.

If you want an example, say you had y = x^2 - 5 and y = 4 as two equations. They have two points of intersection, so when you take one away from the other, at the points intersection the y co-ordinate is 0, so the equation has two distinct solutions, which can be found using the quadratic equation. If there were no intersections originally.. would there be any points where y = 0? (i.e the difference between two y values for both curves for each x value)

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