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 2 years ago
For how many positive integer values of c does the equation below have an integer solution?
 2 years ago
For how many positive integer values of c does the equation below have an integer solution?

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Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge \color{brown}{ 2x^2+689x+c}\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0@TuringTest @phi @hartnn @sauravshakya @shubhamsrg

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0\[(2x+a)(x+b)=4x^2+2x(a+b)+ab\] \[2(a+b)=689,ab=c\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0i dont kow wat to do here

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0first 689 can never be written as even number

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0I am pretty bad at things like this for some reason, sorry.

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0wolfram gives interger solutions as \[c=689n2n^2, x=n\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0I am assuming the equation is\[\large2x^2+689x+c=0\]right?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.12x^2 + 689x + c = 0 c = 689x  2x^2 x= n will always given a ve c, hence x should be n , for some integer n, => c = 689n  2n^2 this has to be >0 => 689n 2n^2 >0 => n(689  2n) >0\ We already know n>0 hence we only have to deal with 689 > 2n or n < 344.5 Hence there can be 344 required value's of c. I have done this on brilliant.org if I am not wrong.

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0yes its from them,i have many other problems from them,if you dont mind you can check the question i asked bfore this one...thanks makes sense

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1What do you mean "the only c" ?

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0the question says For how many positive integer values of c so are there 344 interger c's
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