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\[\huge \color{brown}{ 2x^2+689x+c}\]

\[(2x+a)(x+b)=4x^2+2x(a+b)+ab\]
\[2(a+b)=689,ab=c\]

i dont kow wat to do here

first 689 can never be written as even number

I am pretty bad at things like this for some reason, sorry.

thanks Turing

http://www.wolframalpha.com/input/?i=689

wolfram gives interger solutions as
\[c=689n-2n^2, x=-n\]

I am assuming the equation is\[\large2x^2+689x+c=0\]right?

http://www.wolframalpha.com/input/?i=2x%5E2%2B689x%2Bc%3D0

is this the only c

What do you mean "the only c" ?

the question says
For how many positive integer values of c
so are there 344 interger c's

yes.

okay thanks