# Typo or math error?

#### tiba

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

#### golomorf

Yes. Here your math is perfect. I think there is typo in the text.

#### The Chaz

Forum Staff

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

#### tiba

I understood what you mean, The Chaz, the error was mine after all confusing "double roots" with "two roots"!!

#### CherryPi

Shouldn't "[. . .]have double roots[. . .]" be "[. . .]has double roots[. . .]"? For some reason, it sounds weird with have rather than has.

#### skipjack

Forum Staff
The problem seems to have been slightly inaccurately translated into English prior to being posted.

#### tiba

Actually, skipjack, it was misread by me :roll:, but I don't want to get into Portuguese math terms here hehehe

#### MarkFL

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.