SOLUTION: If the line y + 2x = p does not intersect the curve y^2 = x + p, find the range of values of p

Question 1184258: If the line y + 2x = p does not intersect the curve y^2 = x + p, find the range of values of p
Found 2 solutions by Edwin McCravy, MathLover1:
Answer by Edwin McCravy(20063) (Show Source): You can put this solution on YOUR website!

We solve them simultaneously. If the solutions are real, they will be the values at which they intersect, and if they are imaginary they will not intersect: Solve the first equation for y: Substitute in the second equation: That will not intersect when 24p+1 < 0, or when p < -1/24 Edwin

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

If the line does not intersect the curve , find the range of values of
.......eq.1
..........eq.2
___________________________
.......eq.1
..........eq.2

=> .....square both sides

use discriminant
the line will not intersect the curve if

...., ,

the line will not intersect the curve if

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