User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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: 20,921 Thanks: 2203 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: 20,921 Thanks: 2203 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:
 Originally Posted by Country Boy 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.
And if k = 2, k(k + 1) = 6 so

$6 = -\ 3a^2 \implies a^2 = -\ 2 \implies a = i\sqrt{2}$

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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post shaharhada Calculus 2 December 16th, 2016 07:29 AM GIjoefan1976 Algebra 2 February 15th, 2016 02:56 PM rnck Number Theory 9 May 24th, 2015 03:50 AM Shen Geometry 9 April 14th, 2014 01:21 PM Scrimski Algebra 5 October 10th, 2008 04:57 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      