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Suppose f(x)= (x-8)(x+5)

For which values of x is the function f(x) positive? Enter your answer using inequalities.

 

I believe -5>x>8 is correct? apparently not?

vest4R  Feb 28, 2017

Best Answer 

 #4
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+5

The way to solve these   -always-     is to sketch the graph of the quadratic.I can't use the graphics on this site,but I'll try to explain.

This function is a parabola which touches the x axis at the points (-5,0)  and (8,0). You should sketch it to be clear. When x is less than   -5,f(x)   is positive    and when  x is greater than 8 f(x) is positive.  So you have the UNION of two inequalities, not what you have written above. Answer is ( can't write this in symbols because of software)

 

 x  is les than  (-5)      U       x is greater than 8 

Guest Feb 28, 2017
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 #1
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Hi vest4R,

 

"I believe -5>x>8 is correct? apparently not?"

 

this says

 

-5 is greater than x and x is greater than 8 ...

 

if -5 is greater than x then x must be less than -5

if x is less then -5 how can it be greater than 8  ???

 

See my problem?

Melody  Feb 28, 2017
 #2
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Are you gong to respond to me vest4R ??

Melody  Feb 28, 2017
 #3
avatar+183 
+5

thank you melody, I see what you mean.

 

I'm just trying to work out how to write it now.

vest4R  Feb 28, 2017
 #4
avatar
+5
Best Answer

The way to solve these   -always-     is to sketch the graph of the quadratic.I can't use the graphics on this site,but I'll try to explain.

This function is a parabola which touches the x axis at the points (-5,0)  and (8,0). You should sketch it to be clear. When x is less than   -5,f(x)   is positive    and when  x is greater than 8 f(x) is positive.  So you have the UNION of two inequalities, not what you have written above. Answer is ( can't write this in symbols because of software)

 

 x  is les than  (-5)      U       x is greater than 8 

Guest Feb 28, 2017
 #5
avatar+92484 
0

Thge easiest way to do a question like this is to think about the graph

f(x)= (x-8)(x+5)

 

This is a concave up parabola.  The roots are at  x=8  and  x=-5

 

Since it is concave up it is the bit inbetween these points that falls BELOW the x axis.  and that is where f(x)<0

 

The ends are where f(x)>0

 

so      x<-5    and   x>8

 

here is the graph.

 

Melody  Feb 28, 2017
 #6
avatar+183 
+5

thank you melody. I really appreciate it. The help you give out on this website is top class.

 

It turns out I haven't learned about union's just yet nor did I know they existed.

 Thank you for putting me on the correct path.

vest4R  Feb 28, 2017

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