Expert: Paul Klarreich - 10/19/2007

Question
what is the x-intercept of f(x)= 2x+9%x-7

Answer
Questioner:   Vika
Category:  Advanced Math
Private:  No
 
Subject:  Precalculus
Question:  what is the x-intercept of f(x)= 2x+9%x-7
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Hi, Vika,

That did not come through well.  [See that strange % symbol?]  So I will assume that your finger slipped and you meant just:

f(x)= 2x+9x-7

An x-intercept is also called a 'zero' of the function, and it is a solution to the equation  f(x) = 0.  So solve:

2x + 9x - 7 = 0

Use the quadratic formula, with  a = 2,  b = 9,  c = -7

[Also use courier font to view it.]

   - b +- sqrt(b^2 - 4ac)
x = ----------------------
             2a

   - 9 +- sqrt(81 - 4(2)(-7))
x = --------------------------
             4

   - 9 +- sqrt(81 - 4(2)(-7))
x = --------------------------
             4

   - 9 +- sqrt(81 + 56)
x = ---------------------
             4
 
   - 9 +- sqrt(137)
x = ----------------
          4

Now you have calculator work, but you get your two solutions.  Since they are both real numbers, they are both 'zeroes' of the function and they are both x-intercepts.