Typo or math error?

Jan 2012
52
0
Hello, everyone!

I believe there was an error with the text of the following question, but I just want to make sure my math is perfect here and the text is really wrong:
- Be a a real number so that \(\displaystyle 3y^2 - y + a = 0\) have double roots. So, the solution to the following equation \(\displaystyle 3^{2x+1} - 3^x + a = 0\) is...?

Well, of course the second equation is exactly the same as first, with \(\displaystyle y=3^x\)
Solving, we got: \(\displaystyle 3^x= \frac{1+-sqrt{1-12a}}{6}\)

As none of the answer alternatives is given in terms of a, I suspect the text of the question was wrong and actually that \(\displaystyle 1-12a=0\), giving thus the answer \(\displaystyle x=-\log_{3}{6}\), which is the answer on the answer sheet.

So the text of the question is really:
- Be a a real number so that \(\displaystyle 3y^2 - y + a = 0\) DOESN'T have double roots. So, the solution to the following equation \(\displaystyle 3^{2x+1} - 3^x + a = 0\) is...?

Thanks
 
Jun 2012
59
0
Uzbekistan
Yes. Here your math is perfect. I think there is typo in the text.
 

The Chaz

Forum Staff
Nov 2009
2,767
5
Northwest Arkansas
Wait... So you had access to the answers ahead of time, didn't see "a" in any of the answers, and concluded that there is a typo?

A quadratic having a double root is equivalent to the discriminant (that is, the expression under the radical in the quadratic formula) being equal to zero.

THAT is why you set 1-12a=0
 
Jan 2012
52
0
I understood what you mean, The Chaz, the error was mine after all confusing "double roots" with "two roots"!!
 
Jul 2011
245
0
Shouldn't "[. . .]have double roots[. . .]" be "[. . .]has double roots[. . .]"? For some reason, it sounds weird with have rather than has.
 

skipjack

Forum Staff
Dec 2006
21,473
2,466
The problem seems to have been slightly inaccurately translated into English prior to being posted.
 
Jan 2012
52
0
Actually, skipjack, it was misread by me :roll:, but I don't want to get into Portuguese math terms here hehehe
 
Jul 2010
12,211
522
St. Augustine, FL., U.S.A.'s oldest city
Just to throw my 2 cents in, I would have used in place of the phrase "have double roots" either of the phrases:

i) "has a repeated root"

ii) "has a root of multiplicity 2"

These are the phrasings with which I have become familiar in math texts written in English.