Expert: Paul Klarreich - 2/11/2009

Question
If  f(x) is defined by  -x - 4 / (x + 1). I;ve to find coordinates of where cuts y axis

x = 0  so  (0,-4)   But then told to show that it doesn't cut x axis. The answer says
since x^2 + 4x + 4 = 0 has no real roots (PROBLEM  where do they get x^2 + 4x + 4
Any help greatly appreciated.  Cassie  

Answer
Questioner:   cassie
Category:  Advanced Math
Private:  No
 
Subject:  Function problem
Question:  If  f(x) is defined by  -x - 4 / (x + 1). I;ve to find coordinates of where cuts y axis

x = 0  so  (0,-4)   But then told to show that it doesn't cut x axis. The answer says since x^2 + 4x + 4 = 0 has no real roots (PROBLEM  where do they get x^2 + 4x + 4
Any help greatly appreciated.  Cassie
..........................................................
Your function is:
              4
f(x) = - x - -----
            x + 1

Where does it 'cut' the y-axis?  (Real men say 'intercept'. Real women, too),   That just asks for f(0).  You did that fine.

Now you want to solve  f(x) = 0 for your x-intercepts.
              4
f(x) = - x - ----- = 0  is the equation.
            x + 1

  -4
----- = x
x + 1

- 4 = x^2 + x

x^2 + x + 4 = 0

Now THAT equation does not have real roots.  Easy proof:

b^2 - 4ac, the discriminant = 1 - 16 = -15, so roots are imaginary.

As to your question:
....................
When you wrote:

The answer says since x^2 + 4x + 4 = 0 has no real roots (PROBLEM  where do they get x^2 + 4x + 4?)
.................
you revealed a problem, not with your mathematics, but with your eyesight.  (Want the name of my optometrist?)  

You must have simply misread or miscopied, or maybe there is a misprint in the solution manual for your text.  [The author-professors farm that work out and for what they pay the solution writers, no wonder there are mistakes.]

I hope that helps.