
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 3rd, 2017, 03:46 PM  #1 
Newbie Joined: Jul 2017 From: New Zealand Posts: 7 Thanks: 0  Equal roots of opposite direction
Hi I have a question from a worksheet: For what value(s) of k does the equation 3x^2 + (k  2)x + k(k+1) = 0 have equal roots of opposite direction? Many thanks 
August 3rd, 2017, 03:53 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041 
If the roots are equal, they have the same "direction", whatever "direction" means.

August 3rd, 2017, 04:04 PM  #3 
Newbie Joined: Jul 2017 From: New Zealand Posts: 7 Thanks: 0 
Don't quite understand as that is what appeared in the question...

August 3rd, 2017, 04:26 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041 
The question is misworded or mistyped. If k = 2, the roots are ±√2$\,i$.

August 4th, 2017, 03:23 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
My best guess (and is only a guess) is that the roots are intended to be "a" and "a". Then the equation can be written as 3(x a)(x+ a)= 3x^2 3a^2= 0. Now compare that to the given form, 3x^2+ (k 2)x+ k(k+1)= 0. We must have k 2= 0 so k= 2.

August 4th, 2017, 04:19 AM  #6  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
$6 = \ 3a^2 \implies a^2 = \ 2 \implies a = i\sqrt{2}$ as skipjack said. I guess that answer makes sense if the problem is talking about an Argand plane.  

Tags 
direction, equal, opposite, roots 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
opposite concepts  shaharhada  Calculus  2  December 16th, 2016 07:29 AM 
Two angles in a triangle are equal and their sum is equal to the third angle?  GIjoefan1976  Algebra  2  February 15th, 2016 02:56 PM 
Need Help : to show 2 almost equal fraction is not equal using contradiction??  rnck  Number Theory  9  May 24th, 2015 03:50 AM 
Find the radius of the congruent circle from equal arc and equal chord length  Shen  Geometry  9  April 14th, 2014 01:21 PM 
What is the opposite of unitless?  Scrimski  Algebra  5  October 10th, 2008 04:57 AM 