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

#4**+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

#1**0 **

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

#3**+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**+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**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