0
The point(s) of intersection must satisfy both equations.
So
2x + k = x2 - 8x - 7
Or, x2 - 10x - 7 - k = 0
The discriminant for this quadratic equation is (-10)2 - 4*1*(-7-k)
= 100 + 28 + 4k
= 128 + 4k
For there to be 2 real distinct points of intersection, discriminant > 0
that is 128 + 4k > 0
4k > -128 so that k > -32.
For there to be a single point of intersection, discriminant = 0 so that k = -32.
What else can I help you with?
Is it possible for three points to lie in two distinct planes?
Yes, of course it is.
Can two distinct points both exist on two distinct lines?
No. Two distinct points define a single line.
Can two distinct points define a single line?
All lines are defined by two or more distinct points.
What is a distinct line segment?
It will have end points to be a distinct line segment
How many planes can be made to pass through 3 distinct points?
Infinitely many if the 3 distinct points are collinear. Otherwise just 1.
What is the maximum number of points of intersection when three distinct circles and four distinct lines?
discuss the possible number of points of interscetion of two distinct circle
Is it possible for three points to lie in two distinct planes?
Yes, of course it is.
For any two distinct points A and B AB equals BA is this true?
Yes this true at one point in time
Can two distinct points both exist on two distinct lines?
No. Two distinct points define a single line.
Can two distinct points define a single line?
All lines are defined by two or more distinct points.
What is a distinct line segment?
It will have end points to be a distinct line segment
Do 3 distinct points always lie on the same line?
Yes. Every line has an infinite number of distinct points.
Can two distinct points both exist on two distinct line?
No. Two points determine one line, and only one.
How can you get points on extramarks?
By showing your workings.
How many planes can be made to pass through 3 distinct points?
Infinitely many if the 3 distinct points are collinear. Otherwise just 1.
What is the carat value of 5 points?
Five points equals .5 carats where one carat equals 1.00 points.
How many points determine exactly one line?
It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.
