SOLUTION: Just a bit unsure what this question is asking and how to solve it. 2. Consider the intersection of the functions y=m/10*x + m and y= m/x. Where m is a real number. Investi

Algebra ->  Rational-functions -> SOLUTION: Just a bit unsure what this question is asking and how to solve it. 2. Consider the intersection of the functions y=m/10*x + m and y= m/x. Where m is a real number. Investi      Log On


   

Question 877550: Just a bit unsure what this question is asking and how to solve it.

2. Consider the intersection of the functions y=m/10*x + m and y= m/x. Where m is a real number.

Investigate the values of m that may provide 0, 1 or 2 points of intersection?

And;

3. Consider the intersection of the functions y=mx+4 and y=4/x

Investigate the values of m that may provide 0, 1 or 2 points of intersection?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
2) to find intersection point, set the functions equal to each other.
(m/10)*x + m = m/x
Multiply both sides of = by x
(m/10)*x^2 + mx = m
mx^2/10 +mx = m
Multiply both sides of = by 10
mx^2 + 10mx = 10m
mx^2 + 10mx - 10m = 0
Divide both sides of = by m
x^2 + 10x - 10 = 0
x^2 + 10x + 25 = 10 + 25
(x+5)^2 = 35
x+5 = square root(35)
x = square root(35) - 5
x = -square root (35) - 5
3) mx + 4 = 4/x
Multiply both sides of = by x
mx^2 + 4x = 4
mx^2 + 4x + 4 = 8
m = 1
(x+2)^2 = 8
x+2 = square root (8)
x+2 = 2*square root(2)
x = 2*square root (2) - 2
x = -2*square root (2) - 2