My Math Forum Equal roots of opposite direction

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 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: 18,048 Thanks: 1395 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: 18,048 Thanks: 1395 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: 2,729 Thanks: 705 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
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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.

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