\(\text{If $n$ is a constant and if there exists a unique value of $m$ for which the quadratic equation $x^2 + mx + (m+n) = 0$ has one real solution, then find $n$. }\)
+1712 \(If\ n\ is\ a \ constant\ and\ if\ there\ exists\ a\ unique\ value\ of\ m\ for \\ which\ the\ quadratic\ equation\ x^2 + mx + (m+n) = 0\ has\ one \\ real\ solution,\ then\ find\ n. \)
Sorry The not being able to see the whole problem at once bothered me.
+14915 \({If \ n\ is\ a\ constant\ and\ if\ there\ exists \\ a\ unique\ value\ of\ m\ for\ which\ the\ quadratic\ equation\\ x^2 + mx + (m+n) = 0\ has\ one\ real\ solution,\ then\ find\ n. } \)
\( \color{BrickRed}x^2 + mx + (m+n) = 0\\ x=-\frac{m}{2}\pm\sqrt{(\frac{m}{2})^2-m-n}\ |(p-q-formula)|\)
\((\frac{m}{2})^2-m-n\ge 0\\ n \le\frac{m^2}{4}-m\\ \)
\(n\in\mathbb{R}\ |\ n\le\frac{m^2}{4}-m\)
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