Hdu 5615 Jam's math problem【数学】

Jam's math problem

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 924 Accepted Submission(s): 444

[align=left]Problem Description[/align]
Jam has a math problem. He just learned factorization.

He is trying to factorize ax2+bx+c
into the form of pqx2+(qk+mp)x+km=(px+k)(qx+m).

He could only solve the problem in which p,q,m,k are positive numbers.

Please help him determine whether the expression could be factorized with p,q,m,k being postive.

[align=left]Input[/align]
The first line is a number
T,
means there are T(1≤T≤100)
cases

Each case has one line,the line has 3
numbers a,b,c(1≤a,b,c≤100000000)

[align=left]Output[/align]
You should output the "YES" or "NO".

[align=left]Sample Input[/align]

2
1 6 5
1 6 4

[align=left]Sample Output[/align]

YES
NO

Hint
The first case turn $x^2+6*x+5$ into $(x+1)(x+5)$

题意：

给出一个一元二次方程的一般式的a，b，c 的值，问这个方程是否有整数解

题解：

数学知识：如果一个一元二次方程的判别式是一个整数的完全平方式，那么这个方程必定有整数解（也许这真是个结论吧，网上搜到的此类信息也不多）

/*
一元二次方程有整数解的条件是：
判别式是完全平方数或者完全平方式！
*/
#include<stdio.h>
#include<math.h>
typedef long long ll;
int slove(ll a,ll b,ll c)
{
ll dot=b*b-4*a*c;
if(dot<0)
{
return 0;
}
ll tp=sqrt(dot*1.0);
return tp*tp==dot;
}
int main()
{
int t;
scanf("%d",&t);
while(t--)
{
int a,b,c;
scanf("%d%d%d",&a,&b,&c);
printf("%s\n",slove(a,b,c)?"YES":"NO");
}
return 0;
}