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August 3rd, 2017, 04:46 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, 04:53 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,232 Thanks: 1437 
If the roots are equal, they have the same "direction", whatever "direction" means.

August 3rd, 2017, 05:04 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, 05:26 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,232 Thanks: 1437 
The question is misworded or mistyped. If k = 2, the roots are ±√2$\,i$.

August 4th, 2017, 04:23 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,872 Thanks: 766 
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, 05:19 AM  #6  
Senior Member Joined: May 2016 From: USA Posts: 855 Thanks: 345  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.  

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direction, equal, opposite, roots 
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