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How many integers 'x' are there such that \[x^2 - 3x -19 \] is divisible by 289? :)

28

nd hw did u get that :)

thats wrng btw

ok

no thats not correct :)

don't guess :)

so do u knoe correct answer huh ? ok give me options if u can

yes i knw the answer :D nd this is a subjective question

can u give me options ?

ok
your options are -
a)5
b)9
c)289
d)none of these

u are asking about numbers that are divisible by 289 or only a certain number for x?

m asking that for how many values of x the expression \[x^2 -3x -19 \] is divisible by 289

no one

:) can u give any reason to support your answer?

ganes is typing a reply ...:)

yes :D

yes :) there is another simple method to solve it.

il let others try :)

ok :)

That's pretty clever!

@Astrophysics I love discriminants.

No, it actually means that the roots are not only rational, but integral. :P

clever and neat @ParthKohli

how do you know the top is always even ?

Ahh okay, the only rational roots of \(x^2+bx+c\) are integers by rational root theorem

Oh, that's a good insight. Thanks. Why in the world didn't I think about that... >_<

Wow that is a cool one too! now we have 3 different methods

:)

Hmm, it seems like you guys got the same contradiction in the end. Cool answers.

2nd solution is my fav so far though

Thanks, @geniusie8.