11317번 - Roots! Really? 다국어

A quadratic equation

\[ax^2 + bx + c = 0\]

has two solutions \(x_{+}\) and \(x_{−}\), called roots, which are given by

\[x_{\pm} = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

The two roots may be real or complex, and they may be identical or distinct. Given a quadratic equation and an interval [\(s\), \(t\)] (with \(s\) ≤ \(t\)), we want to know if the equation has a real root in the interval [\(s\), \(t\)]. That is, is it the case that \(s\) ≤ \(r\) ≤ \(t\) where \(r\) is any of the roots \(x_{−}\) or \(x_{+}\)?

The first line of the input contains an integer, N, the number of test cases (1 ≤ N ≤ 1, 000). Then follows N lines, each containing five integers, \(a\), \(b\), \(c\), \(s\), and \(t\), with −10⁷ ≤ \(a\), \(b\), \(c\), \(s\), \(t\) ≤ 10⁷ , \(a\) ≠ 0, and \(s\) ≤ \(t\).

For each of the N test cases, output “Yes” if the equation \(ax^2 + bx + c = 0\) has a real root in the interval [\(s\), \(t\)]. Output “No” otherwise.