Simple Algebra

题意

给定方程\(f(x)=ax^2+bxy+cy^2\)和参数\(a\),\(b\),\(c\)，试确定该方程的取值是否恒非负。

题解

参照文章http://math.mit.edu/~mckernan/Teaching/12-13/Autumn/18.02/l_10.pdf

AC代码

#include <bits/stdc++.h>
#define IO ios::sync_with_stdio(0)
using namespace std;

const int N = 5e2 + 5;

bool check(int a, int b, int c) {
    if (a < 0) return false;
    if (!a) {
        return (!b) && (c >= 0);
    }
    return b * b <= 4 * a * c;
}

int main() {
    IO;
    int a, b, c;
    while (cin >> a >> b >> c) {
        if (check(a, b, c)) cout << "Yes\n";
        else cout << "No\n";
    }
    return 0;
}