web2.0calc
 
+0  
 

 Show that when k =8, f(x)>0 for all values of x

0
3932
3
avatar+845 

\(f(x)= x^2 - (k+8)x + (8k+1)\)

Show that when k =8, f(x)>0 for all values of x

 Oct 20, 2018

3+0 Answers

 #1
avatar+33661 
+3

When k = 8 we have \(f(x) = x^2-16x+64+1 \text{ or } f(x) = (x - 8)^2 + 1\)

 

No matter what the value of x is, (x-8)2 is always zero or positive, Hence f(x) is always greater than zero.

 Oct 20, 2018
edited by Alan  Oct 20, 2018
 #2
avatar+845 
+1

but how do we prove that it is always 0 or positive?

i feel like an explanation is needed for the mark

YEEEEEET  Oct 20, 2018
 #3
avatar+33661 
+1

When x = 8 we have (x-8) = 0

For any other value of x we have (x-8) is either positive or negative. If you square a positive number you get a positive number; if you square a negative number you get a positive number. 

Alan  Oct 20, 2018
edited by Alan  Oct 20, 2018

1 Online Users

Top Users

avatar+118673 Melody moderator
avatar+37146 ElectricPavlov
avatar+33661 Alan moderator
avatar+14995 asinus moderator
avatar+2489 GingerAle
avatar+1908 NotThatSmart
avatar+1839 ABJeIIy
avatar+1768 bader
avatar+1537 parmen
avatar+1443 blackpanther
avatar+1439 kittykat

Sticky Topics