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# Help please, the asnwers are not -56/9, -8 or 4!!

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Let \$r\$ and \$s\$ be the roots of \$3x^2 + 4x - 12 = 0.\$ Find \$r^2 + s^2.\$

Aug 19, 2023

#2
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By Vieta

The sum of the   roots  =  -4 / 3

So

r + s = -4/3          square both sides

r^2  + 2rs + s^2  =  16/9

And the product of the  roots   = -12/ 3 =  -4  = rs

So

2rs = 2 (-4) =  -8

So

r^2 + 2rs + s^2 = 16/9

r^2 - 8 + s^2  = 16/9

r^2 + s^2  =  16/9 + 8  =  88/9

CORRECTED  !!!!....thx to The 3Mathketeers for  catching  my error  !!!!   Aug 19, 2023
edited by CPhill  Aug 30, 2023
edited by CPhill  Aug 30, 2023
#3
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Thanks for trying but those arent' the correct answers

Aug 19, 2023
#4
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I am quite impressed with Cphill's procedure! Unfortunately, Cphill made a mistake when he subtracted 8 from both sides instead of adding 8 to both sides! If you correct that mistake, you should get the right answer!

Unfortunately, this answer is not posting because the AI moderation is not posting it. I will add some filler text because that makes the AI believe that I am writing a complete answer. You, as a reader, need not read further that this sentence.

If I add more filler text, then it is more likely that the AI language model will actually post my answer. At least, that is what I think? I hope I am right because I am just trying to point out an error that I found in one of the most recent answers.

The3Mathketeers  Aug 20, 2023
edited by The3Mathketeers  Aug 20, 2023
edited by The3Mathketeers  Aug 20, 2023