My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree4Thanks
  • 1 Post By skeeter
  • 3 Post By mathman
Reply
 
LinkBack Thread Tools Display Modes
January 12th, 2019, 05:33 AM   #1
Newbie
 
Joined: Jan 2019
From: Bosnia and Herzegovina

Posts: 1
Thanks: 0

I've got solved assignment, but don't understand something

Assignment says: For which k is equation (k-2)x²+2(k-2)x+2=0 doesn't have real solutions?

Solution:
D<0
D=(2(k-2))²-4*2(k-2)
=4(k²-4k+4)-8(k-2)
=4k²-16k+16-8k+16
=4k²-24k+32<0 /:4
=k²-6k+8
k1,2= 6±√4 / 2
k1 = 4 and k2 = 2
and solution is that k∈[2,4)

Now I don't understand why 4 isn't element of k and 2 is?
qu4lizz is offline  
 
January 12th, 2019, 06:38 AM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,805
Thanks: 1449

I do not agree with the given solution.

discriminant must be strictly negative for the quadratic to have no real roots ...

$b^2-4ac < 0$

$4(k-2)^2 - 8(k-2) < 0$

$4(k-2)[(k-2) - 2] < 0$

$4(k-2)(k-4) < 0 \implies k \in (2,4)$
Thanks from topsquark
skeeter is offline  
January 12th, 2019, 06:49 AM   #3
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,621
Thanks: 117

Linear Algebra?
zylo is offline  
January 12th, 2019, 05:12 PM   #4
Global Moderator
 
Joined: May 2007

Posts: 6,660
Thanks: 647

For k=2, the "equation" is 2=0, which has no roots.

for k=4, the equation becomes $x^2+2x+1=0$ which has a real double root at $x=-1$.
Thanks from skeeter, topsquark and qu4lizz

Last edited by mathman; January 12th, 2019 at 05:16 PM. Reason: add material
mathman is offline  
January 13th, 2019, 03:49 PM   #5
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,805
Thanks: 1449

Quote:
Originally Posted by mathman View Post
For k=2, the "equation" is 2=0, which has no roots.

for k=4, the equation becomes $x^2+2x+1=0$ which has a real double root at $x=-1$.
yep ... always look at the original equation. Good catch.
skeeter is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
assignment, solved, understand


« Help x-intercept 2 | - »

Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help Me Kin Assignment mayak201 Physics 5 April 8th, 2018 02:33 PM
Help with an assignment illidan5 Number Theory 5 March 24th, 2016 05:31 AM
Assignment LMW Algebra 1 November 20th, 2012 03:46 PM
Assignment Help ron Calculus 1 October 8th, 2011 10:36 AM





Copyright © 2019 My Math Forum. All rights reserved.